Method, Apparatus and System for Rendering an Information Bearing Function of Time

ABSTRACT

An embodiment of the present invention is directed to a method for partitioning an energy or power source. The energy source may be, for example, a battery or batteries or other power supply or power supplies for an electronic device, such as a cell phone, or mobile device. The energy source (battery for example), or power supply, provides power to a cell phone, or mobile device or any other load or power consuming device. Partitioning this energy source is a technique for controlling its operation so that power is provided to the power consuming device, such as a cell phone more efficiently, thereby extending the length of time the phone can be used between re-charging.

CROSS REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional PatentApplication No. 61/878,867 (Atty. Docket No. 1744.2370000), filed Sep.17, 2013, titled “Method, Apparatus and System for Rendering anInformation Bearing Function of Time,” which is incorporated herein byreference in its entirety.

BACKGROUND

Field

Embodiments of the present invention relate generally to a method,apparatus and system for rendering an information bearing function oftime based on input signals. Embodiments of the present inventionpresent a novel solution to increasing operational battery life andreduced thermal footprint of a cell phone or other communicationsdevice, apparatus, module, subsystem or component by using enhancedinformation distribution and power supply control techniques. Moreparticularly, embodiments of the present invention are directed torendering the information bearing function of time based on efficientinformation distribution and without requiring feedback loops orpre-distortion techniques.

Background Discussion

Currently, cell phones and other mobile communications platforms use anintegral battery as a power source. The power source has limited storagecapacity and users are increasingly demanding better performance fromtheir cell phones. Generally, the cell phone transmitter, andparticularly the power amplifier (PA), consumes a significant amount ofbattery power and generates the most heat when compared with other phonefunctions. The relative battery power demand of the PA is driven by theRF link budget and PA efficiency. The PA is not efficient because ittransmits signals while operating in a substantially linear mode ofoperation. Both high power output and linearity are required to ensurethat the transmissions from the cell phone conform to currently definedindustry standards, and to overcome communication link budget deficits.Unwanted heat is generated by the PA because of inefficiencies in PAoperation.

Generally, PAs operating in a linear mode, are not particularlyefficient, and so, currently, a compromise must be made between batterylife and conformance to the defined industry standards. Since thedefined industry standards are mandatory and inflexible, the reducedbattery life due to the PAs higher power consumption has been expectedas a necessary impact.

Several conventional PA techniques have been developed in an attempt toimprove operational efficiency of cell phones. Some examples of theseconventional techniques include: envelope tracking; pre-distortion;feedback loops; and polar modulation. Other conventional approachesinclude amplification techniques, which include: Class AB poweramplifiers; stage switching amplifiers, or Doherty amplifiers; envelopeelimination and restoration amplifiers (EER); and outphasing and linearamplification with nonlinear components (LILAC) amplifiers. Each ofthese conventional techniques has drawbacks that make it inadequate.Thus, embodiments of the present invention have innovated in a differentdirection to overcome the inadequacies of the conventional approaches.Some conventional approaches are described below.

Envelope Tracking

An objective of envelope tracking is to improve the efficiency of poweramplifiers (PA) carrying high peak-to average-power-ratio (PAPR)signals. The need to achieve high data throughput within limitedspectrum resources requires the use of linear modulation with high peakto average power. Unfortunately, traditional fixed-supply poweramplifiers operating under these conditions have low efficiency. Oneapproach to improve the efficiency of a power amplifier is to vary theamplifier's supply voltage in synchronism with the amplitude envelope ofthe RF signal. This is known as envelope tracking.

Some types of envelope tracking may include: using direct current (DC)to direct current (DC) converters; power DAC (digital analog converter);and Class “AB” push pull video amplifiers. These are some of the methodsused to amplify the amplitude signal. A single amplifier could also beused with Class “A” operation to transfer amplitude information to thecarrier envelope. Unfortunately, this is a very inefficient method totransfer envelope energy to the radio frequency (RF) amplifier. Oftenenvelope tracking is used to make slow adjustments to the DC supply onlywhen envelope fluctuations are of relatively low bandwidth. Such anapparatus is not stable or competitively efficient if modulated at ahigher rate as needed in present-day cell phones.

Another approach is envelope tracking through adjustment of an amplifierpower supply using DC to DC converters. The DC to DC converter output isvaried by its output duty cycle in proportion to a desired energy sothat the resultant filtered voltage level reproduces an amplitudemodulation signal. Unfortunately, a drawback to this approach is that ahigh modulation rate may not be achieved without distortion and/orstability problems.

In some DC to DC tracking converters the efficiency falls as the loadcurrent decreases. This drop is unsatisfactory for optimal modulationrestoration techniques since it usually causes performance to falloutside industry specification requirements. Also, another disadvantageto this approach is that such DC converters often require a large,ferrite core inductor to convert the switched energy to envelop power.This undesirably adds to the complexity and cost of the DC converter.Other semiconductor tradeoffs force the issue of reduced efficiencyversus power output and bandwidth.

Pre-Distortion

Typically, pre-distortion techniques apply a pre-distorted poweramplifier (PA) input signal to a PA. This pre-distorted PA input signalis used to cancel or compensate for inherent distortion of the PA andattempts to improve linearization of the PA. Unfortunately, most digitalimplementations of pre-distortion utilize digital signal processing(DSP) and software, which can cause resource challenges and consumesignificant power associated with the management of current PAs, whichfollow rapid changes in power levels. Moreover, digital implementationsof pre-distortion require significant investment of integrated circuitsilicon area.

Yet another drawback to pre-distortion techniques is the need to inserta nonlinear module (typically known as a “pre-distorter” module) beforethe RF power amplifier. This pre-distorter module counters the nonlinearportion of the PA transfer characteristic. Thus the overall systemresponse from input to the output of the PA is linear when compensatedby the pre-distortion module. The philosophy of this approach identifiesthe PA nonlinearity as an undesirable design limitation or weaknesswhich must be removed. Efficiency is not a primary optimizationparameter for such schemes.

Adaptive digital pre-distortion is a technique that involves digitalimplementation of the pre-distorter module and a feedback loop thatadapts to changes in the response of the PA due to varying operatingconditions. The major drawbacks to this technique are increased powerconsumption, complexity, size and cost of the system due to the adaptivefeedback architecture.

Feedback Loops

As mentioned with respect to pre-distortion above, a feedback loop is acircuit configuration that adapts to changes in the response of the PAdue to varying operating conditions. For example, there is a specifictype of feedback loop known as a “regenerative feedback loop”.

Typically, any RF (radio frequency, which possesses a rate ofoscillation in the range of about 3 kHz to 300 GHz, which corresponds tothe frequency of radio waves, and the alternating currents, which carryradio signals) feedback oscillator can be operated as a regenerativereceiver if modified to provide a controllable reduction in the feedbackloop. It also requires coupling the feedback loop to an incoming signalsource, and coupling audio frequencies out of the feedback loop to asubsequent audio amplification stage.

Unfortunately, feedback loops, including regenerative feedback loops,require additional components and therefore, increase the powerconsumption, complexity, size and cost of the circuit. Also, feedbackloops introduce a number of waveform distortions that must be addressed.Thus, the feedback loops can actually introduce additional noise anderrors into the system. These unwanted imperfections introduced by thefeedback loop result in various waveform contaminations which oftenoffset the benefits.

Polar Modulation

Polar modulation is a modulation technique that uses a modulated signalthat is both phase modulated (PM) and amplitude modulated (AM). In oneexample of polar modulation, the low power modulated signal is splitinto two components: a phase component; and a magnitude component. Thephase and increased magnitude components are then combined using anamplifier.

Unfortunately, polar modulation is an inadequate solution because itrequires a relatively large sample rate compared to the signal Nyquistbandwidth and often requires the use of pre-distortion in the phase andmagnitude. Feedback loops are often employed further complicatingsolutions at a significant cost in efficiency.

In addition to the conventional techniques described above, the field ofpower amplification also includes the use of amplifiers such as: Class“AB” Power Amplifiers; Stage Switching and Doherty Amplifiers; EnvelopeElimination and Restoration (EER) Amplifiers; and Outphasing and LinearAmplification with Nonlinear Components (LINC) Amplifiers. Each of theseamplification techniques suffers drawbacks that make them unsuitable foruse with cell phones.

Class “AB” Power Amplifiers

While Class “AB” Power Amplifiers are a mature and popular technologyfor high production volume RF amplification circuits, such amplifierssuffer numerous drawbacks. For instance, Class “AB” amplifiers achieveonly incremental efficiency gains by adaptive bias control, envelopetracking control, and power supply control. There is a detrimentaltradeoff between linearity and efficiency. “Over-the-Air” specificationsimpose minimum linearity requirements such that precise input powerbackoff is required to balance linearity and efficiency. (“Input powerbackoff” is a reduction of the output power when reducing the inputpower. The efficiency of the power amplifier is reduced due to backoffof the output power, because the amplifier operates in a linear region.)Since input power backoff is waveform dependent, the input power backoffmust be increased for higher peak to average waveforms, which reducesefficiency making Class “AB” amplifiers less than ideal for manyapplications.

Stage Switching Amplifiers and Doherty Amplifiers

Another conventional approach is to use either stage switchingamplifiers or Doherty amplifiers.

Stage switching amplifiers are typically implemented with switches orstaggered bias control, which can be optimized for efficiency atmultiple operating points. Stage switching amplifiers have higheraverage efficiencies than traditional class “AB” power amplifiers whenthe output power range traverses the operating points and suchamplifiers can also be integrated in various semiconductor processes.

Stage switching amplifiers have a number of undesirable drawbacks. Forexample, stage switching amplifiers are normally constructed using Class“AB” stages and therefore, have all of the limitations of Class “AB”power amplifiers, some of which were described above. These drawbacksinclude a tradeoff of linearity versus efficiency and heat dissipation.

Doherty amplifiers are another conventional technique. These amplifiershave increased efficiency for higher peak to average ratio waveforms andthe carrier power amplifier PA is biased Class “B” amplification.Typically, with Doherty amplifiers, the carrier PA alone supplies theoutput power over most of the output power dynamic range. The peaking PAis biased as Class “C” amplification and the peaking PA is “off” duringmost of the output power dynamic range. The peaking PA and carrier PA ofDoherty amplifiers both supply output power during waveform peaks.

Doherty amplifiers suffer numerous undesirable performance drawbacks.For example, they require precise control of the input drive and bias ofthe carrier and peaking PAs (power amplifiers). They also requireprecise impedance values to ensure minimum distortion crossoverperformance as well as having all of the limitations of linear Class “B”power amplifiers. As with the case of stage switching amplifiers,Doherty amplifiers also suffer from linearity versus efficiency tradeoffproblems. Additionally, Doherty amplifiers have inadequacies due toinput backoff considerations, heat dissipation versus linearitytradeoff.

Thus, both stage switching amplifiers and Doherty amplifiers suffer fromnumerous drawbacks, some of which have been discussed above. Thesenumerous drawbacks result in less than desired performance for manyapplications.

Envelope Elimination and Restoration (EER) Amplifiers

EER amplifiers separate the phase and amplitude components from amodulated signal. This type of nonlinear power amplifier technology isemployed in the phase signal path, which has no amplitude component. Theamplitude signal path has no phase component. EER amplifiers can utilizeClass “C”, “D”, “E”, “F” and other nonlinear amplifiers.

EER amplifiers are also referred to as Kahn and/or polar amplifiers andare more efficient than Class “AB” power amplifiers at lower outputpower levels. The EER amplifier permits the bias and power supplyvoltages to be controlled so as to optimize power consumption atdifferent power levels. Theses amplifiers can be largely integrated invarious semiconductor technologies.

However, EER amplifiers (Kahn and/or polar amplifiers) have numerousundesirable characteristics. For example, ERR amplifiers have extremedifficulty maintaining phase signal path and amplitude signal pathalignment. Furthermore, small alignment errors will result in thefailure to pass most ACPR/ACLR requirements. Additionally, EERamplifiers generally require feedback to achieve linearity requirements.These feedback mechanisms typically involve polar feedback with separateamplitude correction and phase correction loops or Cartesian feedbackloops. As discussed above herein, feedback loops greatly reduceamplifier efficiency. The EER amplifiers which utilize DC to DCconverter also require the DC/DC converter bandwidth to be greater thanthe signal bandwidth and are dependent on input waveform linearity. Thisis a serious drawback since input waveforms must significantly exceedthe output linearity requirements.

Another conventional approach has been to use polar amplifiers withCartesian feedback. It requires a complex demodulator (I/Q(In-Phase/Quadrature) Receiver) for the feedback path. Furthermore,using this approach can cause errors in the complex demodulator such asQuadrature and Amplitude imbalance that will be present on the outputsignal. Other drawbacks of this approach include: difficulty maintainingfeedback loop stability due to path delays from the baseband to the RFoutput; the complex demodulator reduces the efficiency; and therequirement that the amplitude envelope reconstruction bandwidth must bemuch greater than the desired output signal bandwidth.

Outphasing and Linear Amplification with Nonlinear Components (LINC)Amplifiers

Outphasing was first proposed by H. Chireix, (“High Power OutphasingModulation,” Proc. IRE, Vol. 23, No. 11, November 1935, pp. 1370-1392 asa method of Generating High Power/High Quality AM Signals with vacuumtubes. Starting around 1975, the term “Outphasing” was supplemented withLINC (Linear Amplification with Nonlinear Components) as the technologywas adopted for use in microwave applications. Outphasing, or LINC, is atechnique that provides In-Phase and Quadrature Phase Baseband Inputsand incorporates transmitter function. It eliminates the traditional RFtransmitter to PA (power amplifier) input interface impedance match,filter, and back-off requirements. LINC is able to utilize multiplenonlinear amplifiers in an attempt to increase amplifier efficiency,favorable thermal characteristics and higher available output power.Indeed LINC does not have any amplitude and phase alignment issues thatEER architectures do and LINC also has a simple transfer function.Another advantage of LINC techniques is that In-Phase and Quadratureinputs are transformed into two or more constant envelope signalcomponents.

White LINC has some advantages, as discussed above, the techniquesuffers serious drawbacks. For example, LINC requires power combinertechnology with the accompanying large physical size (quarter waveelements are 3.75 cm (1.5 inches) at 2 GHz and 7.5 cm (3.0 inches) at 1GHz). Secondly, LINC cannot be integrated without large losses, whichcauses it to be impractical due to semiconductor die size. LINC alsosuffers from a relatively narrow practical application bandwidth.Moreover, parametric and temperature variations adversely affectperformance. LINC has a limited operational temperature range foroptimal performance.

Another significant drawback to LINC techniques is a requirement forisolation between branch power amplifiers. While lossless combiners(reactive elements only) have been used, this creates output waveformdistortions. Simple Pi-networks have also been used and create undesiredoutput waveform distortions.

Referring back to outphasing, the phase accuracy requirements andphysical size are significant drawbacks. For example, at any given powerlevel, to produce quality waveforms, 40 dB of output power dynamic rangeis desirable. Therefore, two sinusoids with perfect amplitude and phasebalance need to vary between 0 degrees phase and 178.86 degrees phase toachieve a 40 dB dynamic power output range. The accuracy required toachieve 40 dB challenges the tolerance of practical circuits in a highvolume application. Thus, this technique is not desirable for currentcell phone applications.

With respect to the large physical size required by outphasing, asmentioned previously, quarter wave elements are 3.75 cm (˜1.5 inches) at2 GHz and 7.5 cm (˜3.0 inches) at I GHz. With such large sizerequirements, this approach currently cannot be integrated without largelosses, whenever quarter wave combiner techniques are used even on asilicon based substrate. Furthermore, it is impractical due tosemiconductor die size. Other drawbacks, similar to those mentionedabove include: narrow bandwidth; having real losses that adverselyaffect efficiency; parametric and temperature variations that adverselyaffect performance; unit-to-unit performance variations thatunexpectedly vary loss, isolation, and center frequency. Additionally,outphasing has a limited temperature range for optimal performance andrequires isolation between power amplifiers. Similar to LINC describedabove, lossless combiners (reactive elements only) have been used andcreate undesired output waveform distortions. Yet another drawback isthat outphasing requires significant branch phase accuracy and branchamplitude accuracy to generate waveforms of acceptable quality.

BRIEF SUMMARY

Embodiments of the present invention are directed to methods, apparatusand systems, as well as components of the methods, apparatus and systemsthat provide blended control, (also known as BLENDED CONTROL BYPARKERVISION™, BLENDED CONTROL BY PARKERVISION™ is a registeredtrademark of ParkerVision, Inc., Jacksonville, Fla.) that enhances powerefficiency or energy efficiency or thermodynamic efficiency (hereaftersimply efficiency unless otherwise stated) for base band and RFmodulation processes. This BLENDED CONTROL BY PARKERVISION™ utilizes aprocess of distributing domains of information to various apparatusmodulation and encoding functions as well as one or more than one energysource to improve efficiency of communications systems, devices, andcomponents including transmitters. This involves the process ofinformation and energy partitioning, associated with a FLUTTER™algorithm, (FLUTTER™ is a registered trademark of ParkerVision, Inc.,Jacksonville, Fla.).

FLUTTER™ organizes input control signals, derived from the informationsource, into domains, which when processed and reintegrated, efficientlyreconstitute a desired modulation and/or encoding. FLUTTER™ dynamicallymanipulates multiple degrees of freedom (v+i) in hardware and/orsoftware, which control the magnitudes and phases of partitions, whilstallocating quantities of information per partition.

One novel embodiment of the present invention includes utilizingFLUTTER™ to render an information bearing function of time, whichincludes waveforms and/or signals and/or a combination of waveforms andsignals, an RF modulated waveform, and/or an RF modulated carriersignal. The FLUTTER™ process includes compositing multiple signals, forexample, three or more signals, to render the information bearingfunction of time, or a representation, or facsimile thereof, such aselectronic data representing the information bearing function of time.These signals may include one or more phase functions and two or moreamplitude functions. The compositing process includes processingconstituent signals substantially simultaneously (or concurrently or inparallel), with each constituent signal assigned a weighting factordependent on the information distributed by the constituent signal, theefficiency associated with the constituent signal statisticaldistribution and the efficiency for reintegrating constituent signals toform a desired information bearing function of time. Compositing mayalso include mapping of one or more signals or portions of one or moresignals to ranges or domains of functions and their subordinate valuesaccording to a dynamic co-variance or cross-correlation of the functionsdistributed within blended controls to an apparatus that generates adesired output signal or signals. The composite statistic of the blendedcontrols is determined by at least one information source withinformation entropy of H(x), the number of the available degrees offreedom for the apparatus, the efficiency of each degree of freedom, andthe corresponding potential to reliably distribute a specific signalrate and information in each degree of freedom. Compositing includes adynamically and statistically weighted calculation of a desired complexsignal in terms of the encoded information, complex cross-correlationsof subordinate functions, compositing signals and minimized waste energyper unit time. Furthermore, the compositing signals may have differentbandwidths, and spectral distributions. The desired output compositedsignal may be an RF carrier signal or a base band signal. The desiredoutput RF carrier or baseband signal may also exist at variable powerlevels.

A communications platform transmitter based on FLUTTER™ and BLENDEDCONTROL BY PARKERVISION™ generates a desired communications signal atthe proper signal level and frequency. The results of employing FLUTTER™and BLENDED CONTROL BY PARKERVISION™ algorithms and architectures areincreased efficiency, lower thermal footprint and universal signalconstruction. For example, using these algorithms and architectures,mobile communications devices can operate longer per battery chargecycle while running cooler. In addition, modern digital communicationsstandards as well as Legacy modulation standards are accommodated.

FLUTTER™ significantly reduces the effective sampling rates and/orbandwidths as well as agile power source resolution critical to certainaspects of signal envelope reconstruction when compared to Legacytechnologies. FLUTTER™ greatly relieves the specification of agile powersupply design used in complex signal envelope construction. Whilecurrent technology approaches seek to increase sample rates andresolution of switched power supplies to increase envelopereconstruction bandwidths and quality, FLUTTER™ enables the minimuminformation distributed to one or more agile power sources utilized aspart of a desired complex signal reconstruction process. Unlike legacytechnologies, average complex envelope sample rates in the power sourcepath may be tailored to fall below the Nyquist reconstruction samplerate using FLUTTER™, if so desired. Compliant signals may be created bythe composite of sparsely sampled power sources with (i) degrees offreedom and additional (v) degrees of freedom within various encodingand modulation functions of the transmitter. Given a certain informationentropy allocated to agile power source utilization, FLUTTER™ is themost efficient approach. The FLUTTER™ algorithm selects from a minimumnumber of specifically tailored power source metrics, distributed atirregular sample intervals of time dependent on envelope statistics,whilst assisting the other degrees of freedom in the transmitter in theprocess of signal envelope construction. Furthermore, this can beaccomplished with an open loop feed forward (OLFF) algorithm if sodesired. The feed forward approach can also be accompanied by a maximumpursuit of nonlinearity in a plurality of parallel algorithm paths tofurther enhance efficiency whilst preserving ultimate output signalintegrity. Legacy approaches such as envelope tracking, Kahn's techniqueand envelope restoration, utilize Nyquist or greater sampling rates,distributing samples at regular intervals of time, in the power supplypath to construct signal envelopes. Often these techniques utilizefeedback algorithms to enhance quality and compensate fornonlinearities, in contrast to FLUTTER™. The sampled power supply valuesare not optimal, like values determined through FLUTTER™. Rather, theyare determined through standard sampling approaches to follow themagnitude of a desired envelope at specific regular sample instants(sample instants are independent of signal envelope statistics) whileinterpolating between these sampled values, primarily using filteringtechnologies.

FLUTTER™, provides the maximum practical efficiency for signal envelopeconstruction given finite energy or power supply resources and thedesire to minimize energy or power supply resource performancerequirements when those resources are dynamic.

One Embodiment: Partitioning an Energy Source

One embodiment of the present invention is directed to a method forpartitioning an energy or power source. The energy source may be, forexample, a battery or batteries or other power supply or power suppliesfor an electronic device, such as a cell phone, or mobile device. Theenergy source (battery for example), or power supply, provides power toa cell phone, or mobile device or any other load or power consumingdevice. Partitioning this energy source is a technique for controllingits operation so that power is provided to the power consuming device,such as a cell phone more efficiently, thereby extending the length oftime the phone can be used between re-charging. Each energy partitionhas one or more associated sample regions. A sample region correspondsto a range of voltage and current, from which metered quantities may beextracted, acquired, generated or sampled and allocated to power theelectronic device, including circuits used for transmission andreception of information bearing functions of time. A sample regionincludes one or more samples that can be used to render a representationof a signal (information bearing function of time). This representationmay be a reconstruction or rendering. The number of partitions and theirassociated metrics are a function of a desired efficiency to render thedesired signal.

In one embodiment of the present invention, the number of partitions isbounded by a desired resolution i≦2^(K) where;

i=number of partitions; and

K=desired resolution for rendering the signal

(information bearing function of time).

Thus, the number of partitions (i) is less than or equal to 2 raised tothe K^(th) power.

A desired signal typically includes information, such as data that isencoded on a waveform.

The signal (information bearing function of time) that is rendered,using the partitioning method described herein, can have an informationentropy value from zero to a maximum value determined by the dynamicrange and ability to access or create resolution of the signal. Theentropy value represents the degree of signal uncertainty; the greaterthe entropy the greater the uncertainty and information content.

The partitioning method described above can also utilize auxiliarydegrees of freedom to determine one or more rendering parameters of aparticular partition. The auxiliary degrees of freedom possess thequality of, for example, a dimension, or dimensions, or subset of adimension, associated with a conceptual mathematical space known asphase space into which energy and/or information can individually orjointly be imparted and represented. Such a phase space may bemulti-dimensional and sponsor multiple degrees of freedom. A singledimension may also support multiple degrees of freedom. There may be anumber, up to and including v, of auxiliary degrees of freedomassociated with each one of the i partitions. i is typically a number ofpower source partitions in a FLUTTER™ algorithm. Thus the v degrees offreedom are associated with other aspects of information encodingfunctions. Hereafter v, i and auxiliary degrees of freedom will bereferred to as desired degrees of freedom unless otherwise stated.

Another embodiment of the present invention is directed toward thepartitioning method described above wherein the partitioning method hasparameters for rendering (i.e. rendering parameters) the signal (i.e.,the information bearing function of time). The rendering parameters orrendering functions may be expressed as, for example, an amplitudefunction, a phase function, a frequency function, or combinations andpermutations of amplitude functions, phase functions and frequencyfunctions. The amplitude function may be, for example, a voltage orcurrent versus time or a discrete set of sample values versus samplenumber or discrete time increment. The phase function may be for examplea phase angle versus time or a discrete set of sample values versussample number or discrete time increment. The frequency function may be,for example, a frequency versus time or a discrete set of sample valuesversus sample number or discrete time increment. Also, amplitude, phase,and frequency may be interrelated by functions. In addition, renderingparameters may also consist of operational constants along with somenumber of rendering functions. Rendering parameters can be obtained andassigned from knowledge of the signal and characterization of theapparatus used for signal construction. Rendering parameters arecoordinated by and distributed by blended controls, which manipulate oneor more degrees of freedom within the apparatus.

Yet another embodiment of the present invention is directed to thepartitioning method described above in which the energy source (forexample, one or more batteries) may be associated with a plurality ofdomains. Domains include a range of values or functions of valuesrelevant to mathematical and/or logical operation or calculation withinthe FLUTTER™ algorithm. Domains may apply to multiple dimensions andtherefore bound hyper-geometric quantities or objects and they mayinclude real and imaginary numbers or sets of mathematical and/orlogical functions or objects. Domains may be identified using subsets ofthe values from (v, i) indices the desirable degrees of freedom for thesystem or apparatus. (v, i) may be used to specify blended controls andassociated functions. Domains may be associated with sub spaces of thephase space.

Yet another embodiment of the present invention is directed to thepartitioning method described above and also utilizes currentdifferentials. These current differentials provide energy to eachpartition in charge increments. In this case differential refers to adifference between some desired value and some preferred referencevalue.

Yet another embodiment of the present invention is directed to thepartitioning method described above and also utilizes electromagnetic(EM) field differentials. These EM field differentials provide energy toeach partition. In this case differential refers to a difference betweensome desired value and some preferred reference value.

Yet another embodiment of the present invention is directed toward thepartitioning method described above wherein the energy source is eithera fixed energy source or a variable energy source. A fixed energy sourceprovides access to a fixed potential or rate of charge from one or moresources. A variable energy source provides access to a variablepotential or rate of charge from one or more sources.

Yet another embodiment of the present invention is directed to thepartitioning method described above and also includes defining a voltagedomain as a function of V_(ξ)−V_(ξ-1)=ΔV_(i) where ξ is a sampleincrement number. The voltage domain may be fixed or adjustable. A fixedvoltage domain does not change. An adjustable voltage domain isadjustable over a range of ΔV_(i), or a multiplicity thereof. Theadjustment may also be based on H(x)_(v,i) or H(x)_(v) _(i) , a set ofentropy functions dependent on a number of transmitter degrees offreedom and power source degrees of freedom. In this instance, v_(i) isan index for blended controls for one or more degrees of freedom withina regulator apparatus, where v is a number of degrees of freedom and iis a power source partition number.

Yet another embodiment of the present invention is directed to thepartitioning method described above and includes using at least aportion of prior knowledge to construct a complex signal envelope. Theprior knowledge is information about the desired signal (informationbearing function of time) that is known prior to the rendering of thesignal. This prior knowledge is used in the partitioning procedure todetermine partition metrics, and may include statisticalcharacterization.

Yet another embodiment of the present invention is directed to thepartitioning method described above and also includes parsing the systeminput information H(x) into constituent information functions H(x)_(v,i)and/or H(x)_(v) _(i) to form domains. Domains may possessjointly-statistically dependent functions of the constituent entropysets H(x)_(v,i) H(x)_(v) _(i) .

Yet another embodiment of the present invention is directed to thepartitioning method described above and also includes adjusting v, iand/or v_(i) based on, signal statistics and apparatus characterization,where v is an index for blended controls for one or more degrees offreedom.

Yet another embodiment of the present invention is directed to thepartitioning method described above, wherein the partitioning stepdescribed above also includes generating a blended control function. Theblended control function can be expressed as function {tilde over(ℑ)}{H(x)_(v) _(i) } and/or {tilde over (ℑ)}{H(x)_(v,i)} where v=1, 2, 3. . . , and i=1, 2, 3, . . . . The blended control function is used toconstruct signals via the control of apparatus degrees of freedom. Theblended control function may use a plurality of paths, includingparallel paths, and may also include at least a partialcross-correlation between related domains.

Yet another embodiment of the present invention is directed to thepartitioning method described above, wherein the blended controlfunction excludes cross-correlation between domains. In this embodiment,the blended control function operates independent of cross-correlation.

Yet another embodiment of the present invention is directed to thepartitioning method described above and also includes calculating and/orapproximating a statistical dependence for the correlations and creatinga composite statistic from the blended controls.

Yet another embodiment of the present invention is directed to thepartitioning method described above and also includes establishing oneor more paths for the partitioning procedure. FLUTTER™ can manipulatepartitions which are based on any relevant dynamic operationalparameter. For example, FLUTTER™ can manipulate energy, momentum,voltage, current, and entropy partitions. Manipulations of thesequantities contain portions of the information of a desired signaldistributed in blended controls to parallel segments of a transmitterapparatus. Information may be encoded in complex values (magnitude andphase) for each blended control path.

Yet another embodiment of the present invention is directed to thepartitioning method described above and also includes switching a powersource or other partition resource at a rate less than a sampling rate.This may also include switching the power source or other partitionresource at a rate less than or equal to the Nyquist rate associatedwith a rendered output signal. This may also include switching a powersupply or other energy partition resource at a rate greater than theNyquist rate. This may include switching a power supply at irregularintervals. This may also include switching a power supply or otherpartition resource at a rate different than the rate used to reconstructan output signal.

Yet another embodiment of the present invention is directed to thepartitioning method described above and also includes establishingsampling rates related to domains. In this embodiment informationentropy and entropy rate within the domain may be used to determine thedomain sampling rate.

Yet another embodiment of the present invention is directed to thepartitioning method described above and also includes establishingdomain bandwidths. Bandwidths associated with processing domains may beless than a rendering bandwidth for a desired output signal.

Yet another embodiment of the present invention is directed to thepartitioning method described above wherein one or more blended controlpaths manipulate energy partitions. The blended control paths can adjustthe relative weight and access to degrees of freedom of any partition.The blended control paths, being dynamic, can vary as the informationbearing function of time evolves.

Yet another embodiment of the present invention is directed to thepartitioning method described above and also includes coordinating atleast two partition paths based on one or more parameters of theinformation bearing function of time. Thus, partition paths may bestructured depending on parameter(s) of the information bearing functionof time (signal). The parameters of the information bearing function oftime include, for example, functions of phase, and/or functions ofamplitude, entropy, and efficiency.

Yet another embodiment of the present invention is directed to thepartitioning method described above and also includes utilizing one ormore partitions based on one or more energy sources.

Yet another embodiment of the present invention is directed to thepartitioning method described above and also utilizes a priorcharacterization of a system response. The prior characterization can beused to determine the number of partitions, their associated metrics andassociated sample rates. As described herein, the prior characterizationof the system response is information about the signal that is knownprior to the rendering of the signal.

Yet another embodiment of the present invention is directed to thepartitioning method described above and also includes coordinating oneor more FLUTTER™ algorithm parameters. These FLUTTER™ algorithmparameters may include, for example, statistics, ranges, domains, logicfunctions and/or metrics. The coordinating is a function of one or moretransmitter parameters. The transmitter parameters may include, forexample, power control states, temperature, power supply levels, antennainterface circuit impedance, waveform statistics, data rate, channelfrequency, GPS coordinates, accelerometer data, compass information, andspatial orientation.

Yet another embodiment of the present invention is directed to thepartitioning method described above, wherein one or more of the energypartitions are statistically allocated. The one or more of the energypartitions are allocated to transition between constellation pointswithin a phase space. The energy partitions are allocated based on aradial difference of an average of a particular portion of phase spacerelative to the phase space center, where a radial value of zero isdesignated as the center position of the phase space. Different energypartitions possess different radial values.

Yet another embodiment of the present invention is directed to thepartitioning method described above, wherein one or more of the energypartitions are allocated based on Peak to Average Power Ratio (PAPR)statistics of the rendered information bearing function of time.

Yet another embodiment of the present invention is directed to thepartitioning method described above and also includes impartinginformation embedded within the functions {tilde over (ℑ)}{H(x)_(v) _(i)} and/or {tilde over (ℑ)}{H(x)_(v,i)} to one or more information domainsfrom one or more information sources to interface to an RF signalmodulation architecture. This information includes any data suitable forapplication.

Yet another embodiment of the present invention is directed to thepartitioning method described above and also includes modifying anoperational state of a power supply during the partitioning procedure.This modification may be for example, turning the power supply “on” or“off”. This modification may also include switching between two or morepower sources during the partitioning procedure. This modification mayalso include adjustment of two or more power sources during thepartitioning procedure.

Yet another embodiment of the present invention is directed to thepartitioning method described above in which one or more partitions areallocated based on efficiency of operation. Efficiency of operation maybe determined by apparatus characterization, rendered signal statistics(such as PAPR), by a process of associating volumes of phase space withassociated domain functions, in part based on rendered parameters. Thisprocess is used to develop blended controls. The blended controls can beused to coordinate partitions.

Another Embodiment: Generating an Information Bearing Function of Time

Yet another embodiment of the present invention is directed to a methodto generate an information bearing function of time. The informationbearing function of time may be, for example, a signal or waveform, RFmodulated signal, representation of a signal, such as electronic datastored on a computer-readable medium, an information bearing energeticfunction of time and space that enables communication, or a modulated RFcarrier waveform, having a dynamic range of approximately between 20 dBto 174 dB. The modulated RF carrier waveform may have one or more powerlevels. This method may be facilitated by storage on a computer-readablemedium, such as software, or RAM (Random Access Memory) ROM (Read OnlyMemory), PROM (Programmable Read Only Memory), EEPROM (ElectricallyErasable Programmable Read Only Memory), non-volatile memory, flashmemory, memory stick, or other suitable electronic storage medium.

This method includes utilizing a mathematical description of modulationand characterization of apparatus based on prior knowledge of theapparatus. This mathematical description or substantially equivalentfunctional representation provides a model suitable for describing themodulation and/or information encoding process of the apparatus. Afunctional description of an original data set is generated and anestimation is also generated. The estimation function represents anapproximation of a deviation from an expected, or desired, function of asignal compared to a signal at the output of the apparatus model. One ormore values for the output information bearing function of time (signal)are calculated based on real-time input samples, apparatuscharacterization and/or real time measurements, and used to develop theestimation function. The real-time input samples are signals or otherinputs received by the system.

Yet another embodiment of the present invention is directed to themethod to generate an information bearing function of time in which themathematical description of modulation includes real and imaginarycomponents. The mathematical description includes digital I and Qcomponents. The I-components include “In-phase” and the Q-componentsinclude “Quadrature-phase”.

Another Embodiment: Rendering a Representation of an Information BearingFunction of Time

Yet another embodiment of the present invention is directed to a methodfor rendering a representation of an information bearing function oftime. The information bearing function of time may be a signal or awaveform, or an RF carrier signal or a modulated RF carrier waveform.

The method includes accessing parameters of a desired informationbearing function of time. These parameters include, for example,amplitude, phase, frequency or functions thereof and may be based onprior system knowledge. Multiple signals are composited to form adesired output signal. Compositing includes, for example, mapping one ormore signals or portions of one or more signals to ranges or domains offunctions and their subordinate values. Mapping is accomplishedaccording to the FLUTTER™ algorithm. FLUTTER™ manages the apparatusfunctions which generate the constituent signals of the blendedcontrols. The composite statistic of the blended controls is determinedby an information source with source entropy of H(x), the number of theavailable degrees of freedom for the apparatus, the efficiency of eachdegree of freedom, and the corresponding potential to distribute aspecific signal rate as well as information rate in each degree offreedom. A representation of the desired information bearing function oftime is rendered based on the compositing step. The rendering may be anoutput signal or waveform, or an electronic representation stored on anelectronic medium, such as a computer-readable medium.

Yet another embodiment of the present invention is directed to themethod for rendering a representation of an information bearing functionof time, as described above, wherein the compositing step includesmanaging a covariance of statistical parameters of constituent signals.Functions of the constituent signals are reintegrated in the compositingprocess to form a desired output signal.

Yet another embodiment of the present invention is directed to themethod for rendering a representation of an information bearing functionof time, as described above, wherein the compositing step includescross-correlations. The cross-correlations are measurements orcalculations of similarity between two or more waveforms and/or signals.

Yet another embodiment of the present invention is directed to themethod for rendering a representation of an information bearing functionof time, as described above, wherein the compositing step includescalculations or measurements of statistical dependencies. Thestatistical dependencies include, for example, a condition in which twoor more random variables are not statistically independent.

Yet another embodiment of the present invention is directed to themethod for rendering a representation of an information bearing functionof time, as described above, wherein the composited signals include oneor more subsets of signals.

Yet another embodiment of the present invention is directed to themethod for rendering a representation of an information bearing functionof time, as described above, wherein compositing consists of a functionof three or more signals. This set of signals may include, for example,two or more amplitude functions and one or more phase functions. Indeed,each of the two or more amplitude functions may have an associatedspectral distribution and respective bandwidths. For example; the firstamplitude function has a first spectral distribution and the secondamplitude function has a second spectral distribution; the firstspectral distribution and bandwidth being different than the secondspectral distribution and bandwidth. In a like manner the multiplicityof phase functions may possess unique spectral distributions andbandwidths.

Yet another embodiment of the present invention is directed to themethod for rendering a representation of an information bearing functionof time, as described above, wherein two or more functions (amplitudeand/or phase) have an associated spectral density. Indeed, a firstfunction has a first spectral density and a second function has a secondspectral density; these first and second spectral densities being atleast partially statistically independent of one another or partiallyuncorrelated.

Yet another embodiment of the present is directed to the method forrendering a representation of an information bearing function of time,as described above, wherein the parameters of a desired informationbearing function of time are based, at least in part, on prior knowledgeobtained by apparatus characterization.

Another Embodiment: Generating an Information Bearing Function of TimeUsing a Synthesizing Step

Yet another embodiment of the present invention is directed to a methodfor generating an information bearing function of time, or arepresentation thereof, that includes identifying one or morecharacteristics of an information bearing function of time. Theinformation bearing function of time may be, for example, a signal,waveform, RF modulated signal, an RF carrier signal, or waverepresentation or composite waveforms. A representation, such as awaveform, signal, data set, electronic rendering or other manifestation,of the information bearing function of time may be synthesized basedupon a composition or compositing of multiple signals.

The composition or compositing includes mapping of one or more signalsor portions of one or more signals to ranges or domains of functions andtheir subordinate values according to a dynamic co-variance orcross-correlation of the functions that distribute blended controls toan apparatus which generates signals. A composite statistic of theblended controls can be determined by an information source with sourceentropy of H(x), the number of the available degrees of freedom for theapparatus, the efficiency of each degree of freedom, and thecorresponding potential to distribute a specific signal rate in andinformation each degree of freedom. The composition may include, forexample: examining covariance of statistical parameters of a signal ofinterest; and cross-correlations and/or calculated and/or measureddependencies.

Yet another embodiment of the present invention is directed toward themethod for generating an information bearing function of time, describedabove wherein the multiple signals include three or more signals. Thethree or more signals include two or more amplitude functions and one ormore phase functions. Indeed, each of the two or more amplitudefunctions has a spectral distribution. For example, a first amplitudefunction has a first spectral distribution and bandwidth and a secondamplitude function has a second spectral distribution and bandwidth; thefirst spectral distribution does not necessarily equal the secondspectral distribution, or the two spectral distributions may be at leastpartially correlated.

Yet another embodiment of the present invention is directed to themethod for generating an information bearing function of time, describedabove wherein parameters of a desired information bearing function oftime are based, at least in part, on prior characterization (priorknowledge) of the apparatus. The prior knowledge may include, forexample, prior known information about the desired information bearingfunction of time, as well as characteristics of an apparatus such asmodulator, encoder or transmitter.

Another Embodiment: Generating an Information Bearing Function ofTime-Accessing Parameters

Yet another embodiment of the present invention is directed to a methodfor generating an information bearing function of time. This methodincludes accessing parameters of a desired information bearing functionof time. These parameters include, for example, amplitude, phase,frequency, or functions thereof. A first subset representation of thedesired information bearing function of time is generated based on oneor more input signals and a first function. The first subsetrepresentation of the desired information bearing function of time iscompared to the parameters of a desired information bearing function oftime and a differential quantity is identified based on the comparison.The input signals are composited with additional one or more inputsignals when the differential quantity exceeds a predetermined thresholdand a second subset representation of the desired information bearingfunction of time is generated based on the compositing step. In thiscase differential refers to a difference between some desired value andsome preferred reference value.

Yet another embodiment of the present invention is directed to themethod described above, wherein the differential quantity is a functionof desirable characteristics of the information bearing function oftime. Indeed, the desirable characteristics of the information bearingfunction of time include one or more of function of amplitude, functionof frequency and/or function of phase.

Yet another embodiment of the present invention is directed to themethod described above and also includes identifying one or morestatistics of amplitude, frequency and/or phase.

Yet another embodiment of the present invention is directed to themethod described above, wherein the parameters of a desired informationbearing function of time are based on prior characterization (priorknowledge) of the apparatus. This apriori or a priori or prior knowledgeincludes information that was known, or identified, prior to therendering of the information bearing function of time.

Yet another embodiment of the present invention is directed to themethod described above, wherein the first subset representation and thesecond subset representation are based on nonlinear functions. Thus, thesubset representations are not linear.

Yet another embodiment of the present invention is directed to themethod described above, wherein the parameters of a desired informationbearing function of time include real and imaginary components that areestablished prior to generating a first subset representation of thedesired information bearing function of time.

Another Embodiment: Optimizing a Power Source

Yet another embodiment of the present invention is directed to a methodfor optimizing the relevant metrics of one or more power sources. Thismethod includes accessing characterizations of an information bearingfunction of time. The information bearing function of time may be, forexample, a signal, waveform, RF modulated signal, an RF carrier signal,or representation or composite waveforms or electronic replicationthereof. A plurality of input sources providing power are accessed.These input power sources also serve as constituent input signals, whichmay be nonlinear and/or switched. Two or more of the input signals arecomposited to generate a representation of the desired outputinformation bearing function of time. This representation may be awaveform, signal, or electronic representation. An operational state ofat least one of the power sources is controlled based on the compositingstep.

Another Embodiment: Apparatus to Control an Energy Source

Yet another embodiment of the present invention is directed to anapparatus to control one or more energy sources. The apparatus includesa storage module adapted to store one or more functions of thecharacteristics of a desired information bearing function of time. Thesefunctions may include, for example, one or more of function ofamplitude, function of frequency and/or function of phase. Theinformation bearing function of time may be, for example, a signal,waveform, RF modulated signal, an RF carrier signal, or representationof composite waveforms.

The apparatus also includes a first module adapted to receive one ormore input signals and provide a first subset of output signals. Asecond module, which is operatively coupled to the first module, isadapted to receive one or more input signals and provide a second subsetof output signals. The first subset of output signals are compositedwith the second subset of output signals to generate a representation ofthe desired information bearing function of time. The compositingincludes mapping of one or more signals or portions of one or moresignals to ranges or domains of functions and their subordinate valuesaccording to a dynamic co-variance or cross-correlation of the functionsthat distribute blended controls to an apparatus which generatessignals. The composite statistic of the blended controls is determinedby an information source with source entropy of H(x), the number of theavailable degrees of freedom for the apparatus, the efficiency of eachdegree of freedom, and the corresponding potential to distribute aspecific signal rate as well as information in each degree of freedom.The compositing process may include, for example: examining covarianceof statistical parameters of a signal of interest; andcross-correlations and/or calculated dependencies.

Yet another embodiment of the present invention is directed to theapparatus described above, wherein the first module and the secondmodule are nonlinear modules. That is, the first and second modulesobtain nonlinear input signals.

Yet another embodiment of the present invention is directed to theapparatus described above and also includes a node, operatively coupledto the second module, adapted to receive the representation of thedesired information bearing function of time and provide a linearrepresentation of the desired information bearing function of time.

Yet another embodiment of the present invention is directed to theapparatus described above, wherein the signal is reconstituted duringcompositing of the one or more first subset of input signals, which arederived from blended controls, and one or more of the second subset ofinput signals, which are derived from blended controls. Thereconstitution is a desired information bearing function of time whichis compliant to a quality metric, often a standard, for example.

Another Embodiment: A Method of Rendering Representation of anInformation Bearing Function of Time

Yet another embodiment of the present invention is directed to a methodfor rendering a representation of an information bearing function oftime. The information bearing function of time may be, for example, asignal, waveform, RF modulated signal, an RF carrier signal, or waverepresentation or composite waveforms or electronic representationthereof.

The method includes utilizing one or more energy sources. These energysources may be, for example, one or more batteries, one or more powersupplies, other power source or sources, or combinations of these energysources. The one or more energy sources are partitioned within selecteddomains to efficiently generate signals used to form a renderedinformation bearing function of time. Domains, for example, include arange of values or functions of values relevant to mathematical and/orlogical operations or calculations within the FLUTTER™ algorithm.Domains may apply to multiple dimensions and therefore boundhyper-geometric quantities and they may include real and imaginarynumbers or any suitable mathematical and/or logical function. Thesignals, which have been generated, are allocated to render therepresentation of the information bearing function of time, such thatthe allocation associates with the change of an operational state of atleast one or more than one of the energy sources. The allocation may becoordinated by a blended control or blended controls, such as BLENDEDCONTROL FUNCTION BY PARKERVISION™ according to a FLUTTER™ algorithm.

Yet another embodiment of the present invention is directed to therendering method described above and also includes iterativelyoptimizing a blending function for the allocation of the input signals.This optimization includes characterization of the implementingapparatus and the information bearing function of time that it rendersand constructing a blended control, such as BLENDED CONTROL FUNCTION BYPARKERVISION™ according to a FLUTTER™ algorithm.

Yet another embodiment of the present invention is directed to therendering method described above, wherein the information bearingfunction of time is a waveform. This waveform is based on a stimulusfunction, which may include the stimulus of some or all of the degreesof freedom, dimensions and domains of the apparatus.

Another Embodiment: Rendering an Information Bearing Function of Time byAccessing Parameters

Yet another embodiment of the present invention is directed to a methodfor rendering a representation of an information bearing function oftime. The method includes accessing parameters of a plurality of desiredinformation bearing functions of time, such as signals, waveforms, RFmodulated signals, and RF carrier signals, or wave representations orcomposite waveforms. The plurality of desired information bearingfunctions of time may be rendered substantially simultaneously (orconcurrently or in parallel). Multiple signals (signal subsets)associated with each of the plurality of desired information bearingfunctions of time are composited. This composition includes, forexample, mapping of one or more signals or portions of one or moresignals to ranges or domains of functions and their subordinate valuesaccording to a dynamic co-variance or cross-correlation of saidfunctions that distribute blended controls to an apparatus whichgenerates signals. The composite statistic of the blended controls isdetermined by an information source with source entropy of H(x), thenumber of the available degrees of freedom for the apparatus, theefficiency of each degree of freedom, and the corresponding potential todistribute a specific signal rate as well as information in each degreeof freedom. A representation of each of the plurality of the desiredinformation bearing functions of time is generated as a part of thecompositing step. This representation may be, for example, a waveform, asignal, an RF modulated signal or electronic data that may be stored onan electronic storage medium, computer-readable medium and/ortransmitted to a remote location via a communication medium, such as anetwork, wireless medium or wired medium.

Another Embodiment: Accounting for Degrees of Freedom

Yet another embodiment of the present invention is directed to a methodthat includes accounting for a number and/or impact of desired degreesof freedom in a system and accounting for a number and/or impact ofundesired degrees of freedom in the system. One or more of the desireddegrees of freedom are excited with energetic waveforms and/or signalsand/or other excitation source. A response by one or more of theundesired degrees of freedom is assessed. This embodiment is used in asystem that has desired degrees of freedom and undesired degrees offreedom. Energy may be applied to the system to excite one or more ofthe desired degrees of freedom. Undesired degrees of freedom will beexcited by the applied energy and a response to the applied energy bythe undesired degrees of freedom can be assessed. Also desired degreesof freedom may be monitored and assessed for corresponding excitations.

Yet another embodiment of the present invention is directed to themethod described above and also includes utilizing priorcharacterization (prior knowledge) of the apparatus and desired signal,apriori information, to identify and/or characterize the desired degreesof freedom. This prior knowledge is previously obtained, or previouslyacquired data about the apparatus and desired information bearingfunction of time prior to final rendering. The desired informationbearing function of time may be, for example, a signal, waveform. RFmodulated signal, an RF carrier signal, or wave representation orcomposite waveforms.

Yet another embodiment of the present invention is directed to themethod described above and also includes characterizing the desireddegrees of freedom for the system. This includes, for example, degreesof freedom that are purposefully designed into the system.

Yet another embodiment of the present invention is directed to themethod described above, wherein the undesired degrees of freedom includeundesirable phenomena scavenging energy. This may include, for example,rotational, translational vibrational, as well as other forms of energy,including apparatus modes which generate heat or any undesirablespurious phenomena. The undesired degrees of freedom include degrees offreedom that are not purposefully designed into the system.

Yet another embodiment of the present invention is directed to themethod described above and also includes identifying and/orcharacterizing a total number of degrees of freedom.

Yet another embodiment of the present invention is directed to themethod described above and also includes estimating a probability orprobabilities that one or more of the undesired degrees of freedom willbe in an excited state or an relatively unexcited state as well as theprobability vs. energy distributed in those states. The effect(s) of oneor more of the undesired degrees of freedom are controlled, ormoderated, utilizing the estimated probability or probabilities. Theprobability or probabilities is/are estimated based on prior, orapriori, apparatus characterization and the statistics of the desiredinformation bearing function of time.

Yet another embodiment of the present invention is directed to themethod described above and also includes identifying one or more thermalcharacteristics to calculate the probability that one or more of theundesired degrees of freedom will be in an excited or unexcited state aswell as the probability vs. energy level distributed in those states.

Another Embodiment: Multiple Input Multiple Output Systems

Yet another embodiment of the present invention is directed to a methodthat includes processing one or more information source inputs, H₁(x),H₂ (x) . . . H_(m)(x), where in is any suitable integer using FLUTTER™and blended control algorithms to produce one or more informationbearing functions of time. Such information bearing functions of time,known also as output signals are enumerated 1, 2 . . . n where n is asuitable integer, are rendered from any number in information sourcesand FLUTTER™ algorithms via blended controls. For example, any number ofm inputs may be mapped to any number of n outputs where m may or may notequal n. Each of the n output signals or alternatively output channelsmay be a result of independent or dependent compositing. That is, eachof the n outputs may share information to any extent required ordesired. This algorithm may be used in applications such as multipleinput multiple output (MIMO) and diversity processing. In addition, nmay be less than in, thus mapping m input information sources to feweroutput signals.

Accordingly, embodiments of the present invention are desired to notencompass any previously known product, process of making the product,or method of using the product such that Applicants reserve the rightand hereby disclose a disclaimer of any previously known product,process, or method. It is further noted that embodiments of the presentinvention do not intend to encompass within the scope of the inventionany product, process, or making of the product or method of using theproduct, which does not meet the written description and enablementrequirements of the USPTO (35 U.S.C. §112, first paragraph) or the EPO(Article 83 of the EPC), such that Applicants reserve the right andhereby disclose a disclaimer of any previously described product,process of making the product, or method of using the product.

It is noted that in this disclosure and particularly in the claimsand/or paragraphs, terms such as “comprises”, “comprised”, “comprising”and the like can have the meaning attributed to it in U.S. Patent law;e.g., they can mean “includes”, “included”, “including”, and the like;and that terms such as “consisting essentially of” and “consistsessentially of have the meaning ascribed to them in U.S. Patent law,e.g., they allow for elements not explicitly recited, but excludeelements that are found in the prior art or that affect a basic or novelcharacteristic of the invention.

These and other embodiments are disclosed or are obvious from andencompassed by, the following Detailed Description.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fees.

To the accomplishment of the foregoing and related ends, certainillustrative aspects of the invention are described herein in connectionwith the following description and the annexed drawings. These aspectsare indicative, however, of but a few of the various ways in which theprinciples of the invention may be employed and embodiments of thepresent invention are intended to include such aspects and theirequivalents. Other advantages, embodiments and novel features of theinvention may become apparent from the following description ofembodiments of the present invention when considered in conjunction withthe drawings. The following description, given by way of example, butnot intended to limit the invention solely to the specific embodimentsdescribed, may be understood in conjunction with the accompanyingdrawings, in which:

FIG. 1 shows a block diagram of inter connect and relation betweenFLUTTER™, blended control and compositing.

FIG. 2 shows a block diagram of a modulator apparatus with blendedcontrols.

FIG. 3 shows a diagram of energy transformation and entropy processingwith blended controls.

FIG. 4 shows a block diagram that illustrates parsing information metricH(x)_(v,i) v=1, 2, 3 . . . n (where “n” is any suitable number), i=1, 2,3 . . . l (where “l” is any suitable number).

FIG. 5 shows a block diagram illustrating modification of H(x) by achannel.

FIG. 6 shows a graphical representation of an approximate GaussianProbability Density Function (pdt) with 0.5 mean.

FIG. 7 shows a graphical representation of an approximate truncatedGaussian Probability Density Function (pdf).

FIG. 8 shows a schematic of a summing node with two input signals and/orwaveforms and one output signal.

FIGS. 9A and 9B show representations of a differential and single endedType I series modulator, respectively, that may be used with embodimentsof the present invention.

FIGS. 10A and 10B show representations of a differential and singleended Type I shunt modulator, respectively, that may be used withembodiments of the present invention.

FIG. 11 shows a graphical representation of an approximately GaussianProbability Density Function (pdf) for output voltage at particularparameters.

FIG. 12 shows a graphical representation of a Probability DensityFunction (pdf) for the instantaneous efficiency of a particular Type Imodulator.

FIG. 13 illustrates a method, using a block diagram, for generating aninformation bearing function of time using blended controls andcompositing.

FIG. 14 illustrates a method, using a block diagram, of generating aninformation bearing function of time using blended controls andcompositing.

FIG. 15 shows an example of a parallel channel configuration to reducePeak Average Power Ratio (PAPR) per branch.

FIG. 16 shows an example of pseudo-phase space samples with threepossible energy partitions.

FIG. 17 shows a graphical representation of an approximate GaussianProbability Density Function (pdf) for output voltage at certainparameters, illustrating an example associated with three energypartitions.

FIG. 18 shows a block diagram of a circuit that transitions as astatistically influenced boundary is traversed.

FIG. 19 shows a graphical representation of instantaneous waveformefficiency as a function of energy partition number for a modulator.

FIG. 20 shows an example of a series Type II modulator.

FIG. 21 shows an example of a shunt Type II modulator.

FIG. 22 illustrates an information and energy partition organization interms of topological signal flow.

FIGS. 23A and 23B show a particular graphical illustration ofdifferential magnitude and differential phase entropy surfaces,respectively.

FIGS. 24A and 24B show a particular graphical illustration of reduceddifferential magnitude and differential phase entropy surfaces,respectively.

FIG. 25 shows an example of a composite statistic of the informationbearing function of time and statistics of domains of signals plotted onvoltage and probability axes.

FIG. 26 shows a flowchart for synthesizing FLUTTER™ and blendedcontrols.

FIG. 27 shows an example of a circuit using FLUTTER™ with (i) fixedpower source partitions and v auxiliary degrees of freedom.

FIG. 28 shows an example of a Thévenized equivalent of FIG. 27.

FIG. 29 shows an example of a circuit using FLUTTER™ with switching orvariable power supplies for one or more of the energy partitions.

FIG. 30 shows of a series equivalent of FIG. 29.

FIG. 31 shows an example of a modulator architecture which may be usedwith the FLUTTER™ algorithm.

FIG. 32 shows an example of a modulator architecture which may be usedwith the FLUTTER™ algorithm.

FIG. 33 shows an example of some signals associated with application ofblended controls as part of the FLUTTER™ algorithm.

FIG. 34 shows an example of some signals associated with application ofblended controls as part of the FLUTTER™ algorithm.

FIG. 35 shows a cascaded switch structure.

FIG. 36 shows a parallel switch topology.

FIG. 37 shows an example of one or more composite information bearingfunctions of time, constructed from one or more information sources,using a FLUTTER™ or blended control based architecture.

FIG. 38 shows an example of two dimensional geometrical structures forforming differential surfaces.

FIG. 39 shows an example of thermodynamic efficiency enhancementperformance plot associated with applications of a FLUTTER™ algorithm toa Type 1 modulator.

DETAILED DESCRIPTION

The embodiments of the invention and the various features andadvantageous details thereof are explained more fully with reference tothe non-limiting embodiments, aspects and examples that are describedand/or illustrated in the accompanying figures and detailed in thefollowing description. It should be noted that the features of oneembodiment or aspect may be employed with other embodiments as theskilled artisan would recognize, even if not explicitly stated herein.The examples used herein are intended merely to facilitate anunderstanding of ways in which the invention may be practiced and tofurther enable those of skill in the art to practice the embodiments ofthe present invention. Accordingly, the examples and embodiments hereinshould not be construed as limiting the scope of the invention, which isdefined solely by the appended claims.

DEFINITIONS

1^(st) Law of Thermodynamics: The first law is often formulated bystating that the change in the internal energy of a closed system isequal to the amount of heat supplied to the system, minus the amount ofwork done by the system on its surroundings. Other forms of energy(including electrical) may be substituted for heat energy in anextension of the first law formulation. The first law of thermodynamicsis an energy conservation law with an implication that energy cannot becreated or destroyed. Energy may be transformed or transported but anumerical calculation of the sum total of energy inputs to an isolatedprocess or system will equal the total of the energy stored in theprocess or system plus the energy output from the process or system. Thelaw of conservation of energy states that the total energy of anisolated system is constant. The first law of thermodynamics isreferenced occasionally as simply the first law.

2^(nd) Law of Thermodynamics: The second law is a basic postulatedefining the concept of thermodynamic entropy, applicable to any systeminvolving measurable energy transfer (classically heat energy transfer).In statistical mechanics information entropy is defined from informationtheory using Shannon's entropy. In the language of statisticalmechanics, entropy is a measure of the number of alternative microscopicconfigurations or states of a system corresponding to a singlemacroscopic state of the system. One consequence of the second law isthat practical physical systems may never achieve 100% thermodynamicefficiency. Also, the entropy of an isolated system will always possessan ever increasing entropy up to the point equilibrium is achieved. Thesecond law of thermodynamics is referred to as simply the second law.

ACPR: Adjacent Channel Power Ratio usually measured in decibels (dB) asthe ratio of an “out of band” power per unit bandwidth to an “in band”signal power per unit bandwidth. This measurement is usuallyaccomplished in the frequency domain. Out of band power is typicallyunwanted.

A.C.: An alternating current which corresponds to a change in thedirection of charge transport and/or the electromagnetic fieldsassociated with moving charge through a circuit. One direction ofcurrent flow is usually labeled as positive and the opposite directionof current flow is labeled as negative and direction of current flowwill change back and forth between positive and negative over time.

Access: Obtain examine or retrieve; ability to use; freedom or abilityto obtain or make use of something.

Account: Record, summarize; keeping a record of; reporting or describingan existence of.

A.C. Coupled: A circuit or system/module is A.C. coupled at isinterfaced to another circuit or system/module if D.C. current cannotpass through the interface but A.C. current or signal or waveform canpass through the interface.

A.C.L.R: Adjacent channel leakage ratio is a measure of how much signalfrom a specific channel allocation leaks to an adjacent channel. In thiscase channel refers to a band of frequencies. Leakage from one band orone channel to another band or channel occurs when signals are processedby nonlinear systems.

A/D: Analog to digital conversion.

Adapt: Modify or adjust or reconstruct for utilization.

Adjust: Alter or change or arrange for a desired result or outcome.

Algorithm: A set of steps that are followed in some sequence to solve amathematical problem or to complete a process or operation such as (forexample) generating signals according to FLUTTER™.

Align: Arrange in a desired formation; adjust a position relative toanother object, article or item, or adjust a quality/characteristic ofobjects, articles or items in a relative sense.

Allocate: Assign, distribute, designate or apportion.

Amplitude: A scalar value which may vary with time. Amplitude can beassociated as a value of a function according to its argument relativeto the value zero. Amplitude may be used to increase or attenuate thevalue of a signal by multiplying a constant by the function. A largerconstant multiplier increases amplitude while a smaller relativeconstant decreases amplitude. Amplitude may assume both positive andnegative values.

Annihilation of Information: Transfer of information entropy intonon-information bearing degrees of freedom no longer accessible to theinformation bearing degrees of freedom of the system and therefore lostin a practical sense even if an imprint is transferred to theenvironment through a corresponding increase in thermodynamic entropy.

Apparatus: Any system or systematic organization of activities,algorithms, functions, modules, processes, collectively directed towarda set of goals and/or requirements: An electronic apparatus consists ofalgorithms, software, functions, modules, and circuits in a suitablecombination depending on application which collectively fulfill arequirement. A set of materials or equipment or modules designed for aparticular use.

Application Phase Space: Application phase space is a higher level ofabstraction than phase space. Application phase space consists of one ormore of the attributes of phase space organized at a macroscopic levelwith modules and functions within the apparatus. Phase space may accountfor the state of matter at the microscopic (molecular) level butapplication phase space includes consideration of bulk statistics forthe state of matter where the bulks are associated with a modulefunction, or degree of freedom for the apparatus.

Approximate: Approximate: almost correct or exact; close in value oramount but not completely precise; nearly correct or exact.

apriori: What can be known based on inference from common knowledgederived through prior experience, observation, characterization and/ormeasurement. Formed or conceived beforehand; relating to what can beknown through an understanding of how certain things work rather than byobservation; presupposed by experience. Sometimes separated as a priori.

Articulating: Manipulation of multiple degrees of freedom utilizingmultiple facilities of an apparatus in a deliberate fashion toaccomplish a function or process.

Associate: To be in relation to another object or thing; linked togetherin some fashion or degree.

Auto Correlation: Method of comparing a signal with or waveform itself.For example, Time—Auto Correlation function compares a time shiftedversion of a signal or waveform with itself. The comparison is by meansof correlation.

Auto Covariance: Method of comparing a signal or waveform with itselfonce the average value of the signal/or waveform is removed. Forexample, a time auto covariance function compares a signal or waveformwith a time shifted version of said signal or waveform.

Bandwidth: Frequency span over which a substantial portion of a signalis restricted or distributed according to some desired performancemetric. Often a 3 dB power metric is allocated for the upper and lowerband (span) edge to facilitate the definition. However, sometimes adiffering frequency span vs. power metric, or frequency span vs. phasemetric, or frequency span vs. time metric, is allocated/specified.Frequency span may also be referred to on occasion as band, or bandwidthdepending on context.

Baseband: Range of frequencies near to zero Hz. and including zero Hz.

Bin: A subset of values or span of values within some range or domain.

Bit: Unit of information measure (binary digit) calculated using numberswith a base 2.

Blended Controls: A set of dynamic distributed control signals generatedas part of the FLUTTER™ algorithm, used to program, configure, anddynamically manipulate the information encoding and modulationfacilities of a communications apparatus.

Blended Control Function: Set of dynamic and configurable controls whichare distributed to an apparatus according to an optimization algorithmwhich accounts for H(x), the input information entropy, the waveformstandard, significant hardware variables and operational parameters.Blended control functions are represented by {tilde over(ℑ)}{H(x)_(v,i)} where v+i is the total number of degrees of freedom forthe apparatus which is being controlled. BLENDED CONTROL BYPARKERVISION™ is a registered trademark of ParkerVision, Inc.,Jacksonville, Fla.

Branch: A path within a circuit or algorithm or architecture.

Bus: One or more than one interconnecting structure such as wires orsignal lines which may interface between circuits or modules andtransport digital or analog information or both.

C: An abbreviation for coulomb, which is a quantity of charge.

Calculate: Solve; probe the meaning of; to obtain the general idea aboutsomething; to determine by a process. Solve a mathematical problem orequation.

Capacity: The maximum possible rate for information transfer through acommunications channel, while maintaining a specified quality metric.Capacity may also be designated (abbreviated) as C, or C with possibly asubscript, depending on context. It should not be confused with Coulomb,a quantity of charge. On occasion capacity is qualified by somerestrictive characteristics of the channel.

Cascading: Transferring or representing a quantity or multiplequantities sequentially.

Transferring a quantity or multiple quantities sequentially.

Cascoding: Using a power source connection configuration to increasepotential energy.

Causal: A causal system means that a system's output response (as afunction of time) cannot precede its input stimulus.

CDF or cdf: Cumulative Distribution Function in probability theory andstatistics, the cumulative distribution function (CDF), describes theprobability that a real-valued random variable X with a givenprobability distribution will be found at a value less than or equal tox. Cumulative distribution functions are also used to specify thedistribution of multivariate random variables. A cdf may be obtainedthrough an integration or accumulation over a relevant pdf domain.

Characterization: Describing the qualities or attributes of something.The process of determining the qualities or attributes of an object, orsystem.

Channel Frequency: The center frequency for a channel. The centerfrequency for a range or span of frequencies allocated to a channel.

Charge: Fundamental unit in coulombs associated with an electron orproton, ˜±1.602×10⁻¹⁹ C., or an integral multiplicity thereof.

Code: A combination of symbols which collectively possess an informationentropy.

Communication: Transfer of information through space and time.

Communications Channel: Any path possessing a material and/or spatialquality that facilitates the transport of a signal.

Communications Sink: Targeted load for a communications signal or anapparatus that utilizes a communication signal. Load in thiscircumstance refers to a termination which consumes the applicationsignal and dissipates energy.

Complex Correlation: The variables which are compared are represented bycomplex numbers. The resulting metric may have a complex number result.

Complex Number: A number which has two components; a real part and animaginary part. The imaginary part is usually associated with amultiplicative symbol i) or j) which has a value √{square root over(−1)}. The numbers are used to represent values on two different numberlines and operations or calculations with these numbers require the useof complex arithmetic. Complex arithmetic and the associated numbers areused often in the study signals, mathematical spaces, physics and manybranches of science and engineering.

Complex Signal Envelope: A mathematical description of a signal, x(t),suitable for RF as well as other applications. The various quantitiesand relationships that follow may be derived from one another usingvector analysis and trigonometry as well as complex arithmetic.

x(t) = a(t)^(j(ω_(c)t + φ(t)))x(t) = a_(i)(t)cos (ω_(c)t + φ(t)) − a_(Q)(t)sin (ω_(c)t + φ(t))ω_(c) ≡ Carrier  Frequency φ(t) ≡ Phase  Information  vs. Timea(t) ≡ Amplitude  Information  vs. Time${{a(t)}} = \sqrt{{a_{I}^{2}(t)} + {a_{Q}^{2}(t)}}$${\varphi (t)} = {{{arc}\mspace{11mu} {{{\tan \;\left\lbrack \frac{a_{Q}(t)}{a_{I}(t)} \right\rbrack}\;\lbrack{sign}\rbrack}\lbrack{sign}\rbrack}} \equiv {A\mspace{14mu} {function}\mspace{14mu} {which}\mspace{14mu} {accounts}\mspace{14mu} {for}\mspace{14mu} {the}\mspace{14mu} {quadrant}}}$of  φ(t)  in  the  complex  signal/waveform  plane. Sometimesreferred  to  as  complex  envelope  or  simply  envelope.

Compositing: The mapping of one or more constituent signals or portionsof one or more constituent signals to domains and their subordinatefunctions and arguments according to a FLUTTER™ algorithm. Blendedcontrols developed in the FLUTTER™ algorithm, regulate the distributionof information to each constituent signal. The composite statistic ofthe blended controls is determined by an information source with sourceentropy of H(x), the number of the available degrees of freedom for theapparatus, the efficiency of each degree of freedom, and thecorresponding potential to distribute a specific signal rate, as well asinformation, in each degree of freedom.

Consideration: Use as a factor in making a determination.

Constellation: Set of coordinates in some coordinate system with anassociated pattern.

Constellation Point: A single coordinate from a constellation.

Constituent Signal: A signal which is part of a parallel processing pathin FLUTTER™ and used to form more complex signals through compositing orother operations.

Coordinate: A value which qualifies and/or quantifies position within amathematical space. Also may possess the meaning; to manage a process.

Correlation: The measure by which the similarity of two or morevariables may be compared. A measure of 1 implies they are equivalentand a measure of 0 implies the variables are completely dissimilar. Ameasure of (−1) implies the variables are opposite or inverse. Valuesbetween (−1) and (+1) other than zero also provide a relative similaritymetric.

Covariance: This is a correlation operation between two different randomvariables for which the random variables have their expected values oraverage values extracted prior to performing correlation.

Create: To make or produce or cause to exist; to being about; to bringinto existence. Synthesize, generate.

Cross-Correlations: Correlation between two different variables.

Cross-Covariance: Covariance between two different random variables.

Current: The flow of charge per unit time through a circuit.

d2p™: Direct to Power (Direct2Power™) a registered trademark ofParkerVision Inc., corresponding to a proprietary RF modulator andtransmitter architecture and modulator device.

DIA: Digital to Analog conversion.

Data Rates: A rate of information flow per unit time.

D.C.: Direct Current referring to the average transfer of charge perunit time in a specific path through a circuit. This is juxtaposed to anAC current which may alternate directions along the circuit path overtime. Generally a specific direction is assigned as being a positivedirect current and the opposite direction of current flow through thecircuit is negative.

D.C. Coupled: A circuit or system/module is D.C. coupled at itsinterface to another circuit or system/module if D.C. current or aconstant waveform value may pass through the interface.

DCPS: Digitally Controlled Power or Energy Source

Decoding: Process of extracting information from an encoded signal.

Decoding Time: The time interval to accomplish a portion or all ofdecoding.

Degrees of Freedom: A subset of some space (for instance phase space)into which energy and/or information can individually or jointly beimparted and extracted according to qualified rules which may determinecodependences. Such a space may be multi-dimensional and sponsormultiple degrees of freedom. A single dimension may also supportmultiple degrees of freedom. Degrees of freedom may possess anydependent relation to one another but are considered to be at leastpartially independent if they are partially or completely uncorrelated.Degrees of freedom also possess a corresponding realization in theinformation encoding and modulation functions of a communicationsapparatus. Different mechanisms for encoding information in theapparatus may be considered as degrees of freedom.

Delta Function: In mathematics, the Dirac delta function, or S function,is a generalized function, or distribution, on the real number line thatis zero everywhere except at the specified argument of the function,with an integral equal to the value one when integrated over the entirereal line. A weighted delta function is a delta function multiplied by aconstant or variable.

Density of States for Phase Space: Function of a set of relevantcoordinates of some mathematical, geometrical space such as phase spacewhich may be assigned a unique time and/or probability, and/orprobability density. The probability densities may statisticallycharacterize meaningful physical quantities that can be furtherrepresented by scalars, vectors and tensors.

Derived: Originating from a source in a manner which may be confirmed bymeasure, analysis, or inference.

Desired Degree of Freedom: A degree of freedom that is efficientlyencoded with information. These degrees of freedom enhance informationconservation and are energetically conservative to the greatestpractical extent. They are also known as information bearing degrees offreedom. These degrees of freedom may be deliberately controlled ormanipulated to affect the causal response of a system through, andapplication of, algorithm or function such as a blended control functionenabled by a FLUTTER™ algorithm.

Dimension: A metric of a mathematical space. A single space may have oneor more than one dimension. Often, dimensions are orthogonal. Ordinaryspace has 3-dimensions; length, width and depth. However, dimensions mayinclude time metrics, code metrics, frequency metrics, phase metrics,space metrics and abstract metrics as well, in any suitable quantity orcombination.

Domain: A range of values or functions of values relevant tomathematical or logical operations or calculations. Domains mayencompass processes associated with one or more degrees of freedom andone or more dimensions and therefore bound hyper-geometric quantities.Domains may include real and imaginary numbers, and/or any set oflogical and mathematical functions and their arguments.

Encoding: Process of imprinting information onto a waveform to create aninformation bearing function of time.

Encoding Time: Time interval to accomplish, a portion or all, encoding.

Energy: Capacity to accomplish work where work is defined as the amountof energy required to move an object or associated physical field(material or virtual) through space and time. Energy may be measured inunits of Joules.

Energy Function: Any function that may be evaluated over its argumentsto calculate the capacity to accomplish work, based on the functionarguments. For instance, energy may be a function of time, frequency,phase, samples, etc. When energy is a function of time it may bereferred to as instantaneous power or averaged power depending on thecontext and distribution of energy vs. some reference time interval. Onemay interchange the use of the term power and energy given implied orexplicit knowledge of some reference interval of time over which theenergy is distributed. Energy may be quantified in units of Joules.

Energy Partition: A function of a distinguishable gradient field, withthe capacity to accomplish work. Partitions may be specified in terms offunctions of energy, functions of power, functions of current, functionsof voltage, or some combination of this list.

Energy partitions are distinguished by distinct ranges of variableswhich define them. For instance, out of i possible energy domains thek^(th) energy domain may associate with a specific voltage range orcurrent range or energy range or momentum range . . . etc.

Energy Source or Sources: A device or devices which supplies or supplyenergy from one or more access nodes of the source or sources to one ormore apparatuses. One or more energy sources may supply a singleapparatus. One or more energy sources may supply more than oneapparatus.

Entropy: Entropy is an uncertainty metric proportional to the logarithmof the number of possible states in which a system may be foundaccording to the probability weight of each state.

{For example: Information entropy is the uncertainty of an informationsource based on all the possible symbols from the source and theirrespective probabilities.}

{For example: Physical entropy is the uncertainty of the states for aphysical system with a number of degrees of freedom. Each degree offreedom may have some probability of energetic excitation.}

Equilibrium: Equilibrium is a state for a system in which entropy isstable, i.e., no longer changing.

Ergodic: Stochastic processes for which statistics derived from timesamples of process variables correspond to the statistics of independentensembles selected from the process. For ergodic ensemble, the averageof a function of the random variables over the ensemble is equal withprobability unity to the average over one or more possible timetranslations of a particular member function of the ensemble, except fora subset of representations of measure zero. Although processes may notbe perfectly ergodic they may be suitably approximated as so under avariety of practical circumstances.

Ether: Electromagnetic transmission medium, usually ideal free spaceunless otherwise implied. It may be considered as an example of aphysical channel.

EVM: Error Vector Magnitude applies to a sampled signal that isdescribed in vector space. The ratio of power in the unwanted variance(or approximated variance) of the signal at the sample time to the rootmean squared power expected for a proper signal.

Excited: A stimulated state or evidence of a stimulated state relativeto some norm.

Feedback: The direction of signal flow from output to input of a circuitor module or apparatus. Present output values of such architectures ortopologies are returned or “fed back” to portions of the circuit ormodule in a manner to influence future outputs using control loops.Sometimes this may be referred to as closed loop feed forward (CLFF) toindicate the presence of a control loop in the architecture.

Feed forward: The direction of signal flow from input to output of acircuit or module or apparatus. Present output values of sucharchitectures or topologies are not returned or “fed back” to portionsof the circuit or module in a manner to influence future outputs usingcontrol loops. Sometimes this may be referred to as open loop feedforward (OLFF) to indicate the absence of a control loop in thearchitecture.

FLUTTER™: Algorithm which manages one or more of the degrees of freedomof a system to efficiently distribute energy via blended controlfunctions to functions/modules within a communications apparatus.FLUTTER™ is a registered trademark of ParkerVision, Inc. Jacksonville,Fla.

Frequency: (a) Number of regularly occurring particular distinguishableevents per unit time, usually normalized to a per second basis. Numberof cycles or completed alternations per unit time of a wave oroscillation, also given in Hertz (Hz) or radians per second (in thiscase cycles or alternations are considered events). The events may alsobe samples per unit time, pulses per unit time, etc. An average rate ofevents per unit time.

(b) In statistics and probability theory the term frequency relates tohow often or how likely the occurrence of an event is relative to sometotal number of possible occurrences. The number of occurrences of aparticular value or quality may be counted and compared to some totalnumber to obtain a frequency.

Frequency Span: Range of frequency values. Band of frequency values.Channel.

Function of: ℑ{ } or {tilde over (ℑ)}{ } are used to indicate a“function of” the quantity or expression (also known as argument) in thebracket { }. The function may be a combination of mathematical and/orlogical operation.

Harmonic: Possessing a repetitive or rhythmic quality, rhythm orfrequency which may be assigned units of Hertz (Hz) or radians persecond (rad/s) or integral multiples thereof. For instance a signal witha frequency of f_(c) possesses a first harmonic of 1f_(c) Hz, a secondharmonic of 2f_(c) Hz, a third harmonic of 3f_(c) Hz, so on and soforth. The frequency 1f_(c) Hz or simply f_(c). Hz is known as thefundamental frequency.

Hyper-Geometric Manifold: Mathematical surface described in a space with4 or more dimensions. Each dimension may also consist of complexquantities.

Impedance: A measure to the opposition of time varying current flow in acircuit. The impedance is represented by a complex number with a realpart or component also called resistance and an imaginary part orcomponent also called a reactance. The unit of measure is ohms.

Imprint: The process of replicating information, signals, patterns, orset of objects. A replication of information, signals, patterns, or setof objects.

Information: A message (sequence of symbols) contains a quantity ofinformation determined by the accumulation of the following; thelogarithm of a symbol probability multiplied by the negative of thesymbol probability, for one or more symbols of the message. In this casesymbol refers to some character or representation from a source alphabetwhich is individually distinguishable and occurs with some probabilityin the context of the message. Information is therefore a measure ofuncertainty in data, a message or the symbols composing the message. Thecalculation described above is an information entropy measure. Thegreater the entropy the greater the information content. Information canbe assigned the units of bits or nats depending on the base of thelogarithm.

In addition, for purpose of disclosure information will be associatedwith physical systems and processes, as an uncertainty of events fromsome known set of possibilities, which can affect the state of a dynamicsystem capable of interpreting the events. An event is a physical actionor reaction which is instructed or controlled by the symbols from amessage.

Information Bearing: Able to support the encoding of information. Forexample, information bearing degrees of freedom are degrees of freedomwhich may be encoded with information.

Information Bearing Function: Any set of information samples which maybe indexed.

Information Bearing Function of Time: Any waveform, that has beenencoded with information and therefore becomes a signal. Related indexedvalues may be assigned in terms of some variable encoded withinformation vs. time.

Information Entropy: H(p(x)) is also given the abbreviated notation H(x)and refers to the entropy of a source alphabet with probability densityp(x), or the uncertainty associated with the occurrence of symbols (x)from a source alphabet. The metric H(x) may have units of bits orbits/per second depending on context but is defined by

$H = {(x){\sum\limits_{i}\; {{- {p\left( x_{i} \right)}}{\log_{b}\left( {p\left( x_{i} \right)} \right)}}}}$

in the case where p(x)_(i) is a discrete random variable. If p(x) is acontinuous random variable then;

${H(x)} = {- {\int{{p(x)}\mspace{11mu} \log_{b}\frac{{p(x)}{x}}{m(x)}}}}$

Using mixed probability densities, mixed random variables, both discreteand continuous entropy functions may apply with a normalized probabilityspace of measure 1. Whenever b=2 the information is measured in bits. Ifb=e then the information is given in nats. H(x) may often be used toquantity an information source. (On occasion H(x), H_(x) or its otherrepresentations may be referred to as “information”, “informationuncertainty” or “uncertainty”. It is understood that a quantity ofinformation, its entropy or uncertainty is inherent in such a shorthandreference.

Information Stream: A sequence of symbols or samples possessing aninformation metric. For instance, a code is an example of an informationstream. A message is an example of an information stream.

Input Sample: An acquired quantity or value of a signal, waveform ordata stream at the input to a function, module, apparatus, or system.

Instantaneous: Done, occurring, or acting without any perceptibleduration of time; Accomplished without any delay being purposelyintroduced; occurring or present at a particular instant.

Instantaneous Efficiency: This is a time variant efficiency obtainedfrom the ratio of the instantaneous output power divided by theinstantaneous input power of an apparatus, accounting for statisticalcorrelations between input and output. The ratio of output to inputpowers may be averaged.

Integrate: This term can mean to perform the mathematical operation ofintegration or to put together some number of constituents or parts toform a whole.

Interface: A place or area where different objects or modules orcircuits, meet and communicate or interact with each other or values orattributes or quantities are exchanged.

Intermodulation Distortion: Distortion arising from nonlinearities of asystem. These distortions may corrupt a particular desired signal as itis processed through the system.

Iterative: Involving repetition. Involving repetition while incrementingvalues, or changing attributes.

k_(B): (See Boltzmann's Constant)

Line: A geometrical object which exists in two or more dimensions of areferenced coordinate system. A line possesses a continuous specificsequence of coordinates within the reference coordinate system and alsopossesses a finite derivative at every coordinate (point) along itslength. A line may be partially described by its arc length and radiusof curvature. The radius of curvature is greater than zero at all pointsalong its length. A curved line may also be described by the tip of aposition vector which accesses each point along the line for aprescribed continuous phase function and prescribed continuous magnitudefunction describing the vector in a desired coordinate system.

Line Segment: A portion of a line with a starting coordinate and anending coordinate.

Linear: Pertaining to a quality of a system to convey inputs of a systemto the output of the system. A linear system obeys the principle ofsuperposition.

Linear Operation: Any operation of a module system or apparatus whichobeys the principle of superposition.

LO: Local Oscillator

Logic: A particular mode of reasoning viewed as valid or faulty, asystem of rules which are predictable and consistent.

Logic Function: A circuit, module, system or processor which appliessome rules of logic to produce an output from one or more inputs.

Macroscopic Degrees of Freedom: The unique portions of application phasespace possessing separable probability densities that may be manipulatedby unique physical controls derivable from the function {tilde over(ℑ)}{H(x)_(v) _(i) } and/or {tilde over (ℑ)}{H(x)_(v,i)} sometimesreferred to as blended controls or blended control signals. Thisfunction takes into consideration, or accounts for, desired degrees offreedom and undesired degrees of freedom for the system. These degreesof freedom (undesired and desired) can be a function of system variablesand may be characterized by prior knowledge of the apparatus a prioriinformation.

Magnitude: A numerical quantitative measurement or value proportional tothe square root of a squared vector amplitude.

Manifold: A surface in 3 or more dimensions which may be closed.

Manipulate: To move or control; to process using a processing device oralgorithm:

Mathematical Description: Set of equations, functions and rules based onprinciples of mathematics characterizing the object being described.

Message: A sequence of symbols which possess a desired meaning orquantity and quality of information.

Metrics: A standard of measurement; a quantitative standard orrepresentation; a basis for comparing two or more quantities. Forexample, a quantity or value may be compared to some reference quantityor value.

Microscopic Degrees of Freedom: Microscopic degrees of freedom arespontaneously excited due to undesirable modes within the degrees offreedom. These may include, for example, unwanted Joule heating,microphonics, photon emission, electromagnetic (EM) field emission and avariety of correlated and uncorrelated signal degradations.

MIMO: Multiple input multiple output system architecture.

MISO: Multiple input single output operator.

Mixture: A combination of two or more elements; a portion formed by twoor more components or constituents in varying proportions. The mixturemay cause the components or constituents to retain their individualproperties or change the individual properties of the components orconstituents.

Mixed Partition: Partition consisting of scalars, vectors tensors withreal or imaginary number representation in any combination.

MMSE: Minimum Mean Square Error. Minimizing the quantity

({tilde over (X)}−X)²

where {tilde over (X)} is the estimate of X, a random variable. {tildeover (X)} is usually an observable from measurement or may be derivedfrom an observable measurement, or implied by the assumption of one ormore statistics.

Modes: The manner in which energy distributes into degrees of freedom.For instance, kinetic energy may be found in vibrational, rotational andtranslation forms or modes. Within each of these modes may exist one ormore than one degree of freedom. In the case of signals for example, themode may be frequency, or phase or amplitude, etc., Within each of thesesignal manifestations or modes may exist one or more than one degree offreedom.

Modify: To change some or all of the parts of something.

Modulation: A change in a waveform, encoded according to information,transforming the waveform to a signal.

Modulation Architecture: A system topology consisting of modules and/orfunctions which enable modulation.

Modulated Carrier Signal: A sine wave waveform of some physical quantity(such as current or voltage) with changing phase and/or changingamplitude and/or changing frequency where the change in phase andamplitude are in proportion to some information encoded onto the phaseand amplitude. In addition, the frequency may also be encoded withinformation and therefore change as a consequence of modulation.

Module: A processing related entity, either hardware, software, or acombination of hardware and software, or software in execution. Forexample, a module may be, but is not limited to being, a process runningon a processor or microprocessor, an object, an executable, a thread ofexecution, a program, and/or a computer. One or more modules may residewithin a process and/or thread of execution and a module may belocalized on one chip or processor and/or distributed between two ormore chips or processors. The term “module” also means software code,machine language or assembly language, an electronic medium that maystore an algorithm or algorithms or a processing unit that is adapted toexecute program code or other stored instructions. A module may alsoconsist of analog, or digital and/or software functions in somecombination or separately. For example an operational amplifier may beconsidered as an analog module.

Multiplicity: The quality or state of being plural or various.

Nat: Unit of information measure calculated using numbers with a naturallogarithm base.

Node: A point of analysis, calculation, measure, reference, input oroutput, related to procedure, algorithm, schematic, block diagram orother hierarchical object. Objects, functions, circuits or modulesattached to a node of a schematic or block diagram access the samesignal and/or function of signal common to that that node.

Non Central: As pertains to signals or statistical quantities; thesignals or statistical quantities are characterized by nonzero meanrandom processes or random variables.

Non-Excited: The antithesis of excited. (see unexcited)

Non-Linear: Not obeying the principle of super position. A system orfunction which does not obey the superposition principle.

Non-Linear Operation: Function of an apparatus, module, or system whichdoes not obey superposition principles for inputs conveyed through thesystem to the output.

Nyquist Rate: A rate which is 2 times the maximum frequency of a signalto be reproduced by sampling.

Nyquist—Shannon Criteria: Also called the Nyquist-Shannon samplingcriteria;

requires that the sample rate for reconstructing a signal oracquiring/sampling a signal be at least twice the bandwidth of thesignal (usually associated as an implication of Shannon's work). Undercertain conditions the requirement may become more restrictive in thatthe required sample rate may be defined to be twice the frequency of thegreatest frequency of the signal being sampled, acquired orreconstructed (usually attributed to Nyquist). At baseband, bothinterpretations apply equivalently. At pass band it is theoreticallyconceivable to use the first interpretation, which affords the lowestsample rate.

Object: Some thing, function, process, description, characterization oroperation. An object may be abstract or material, of mathematicalnature, an item or a representation depending on the context of use.

Obtain: To gain or acquire.

“on the fly”: This term refers to a substantially real time operationwhich implements an operation or process with minimal delay maintaininga continuous time line for the process or operation. The response toeach step of the operation, or procedure organizing the operation,responds in a manner substantially unperceived by an observer comparedto some acceptable norm.

Operation: Performance of a practical work or of something involving thepractical application of principles or processes or procedure; any ofvarious mathematical or logical processes of deriving one entity fromothers according to a rule. May be executed by one or more processors orprocessing modules or facilities functioning in concert orindependently.

Operational State: Quantities which define or characterize an algorithm,module, system or processor a specific instant.

Operatively Coupled: Modules or Processors which depend on their mutualinteractions.

Optimize: Maximize or Minimize one or more quantities and/or metrics offeatures subject to a set of constraints.

PAER: Peak to Average Energy Ratio which can be measured in dB ifdesired. It may also be considered as a statistic or statisticalquantity for the purpose of this disclosure. It is obtained by dividingthe peak energy for a signal or waveform by its average energy.

PAPR: Peak to Average Power Ratio which can be measured in dB ifdesired. For instance PAPR is the peak to average power of a signal orwaveform determined by dividing the instantaneous peak power excursionfor the signal or waveform by its average power value. It may also beconsidered as a statistic or statistical quantity for the purpose ofthis disclosure.

Peak to Average Power Ratio which can be measured in dB if desired. Forinstance PAPR_(sig) is the peak to average power of a signal determinedby dividing the instantaneous peak power excursion for the signal by itsaverage power value. It may also be considered as a statistic orstatistical quantity for the purpose of this disclosure

Parallel Paths: A multiplicity of paths or branches possessing theattribute of a common direction of signal or process flow through amodule, circuit, system or algorithm. In a simple case parallel pathsmay possess a comment source terminal or node and a common ending nodeor terminus. Each path or branch may implement unique processor orsimilar processes.

Parameter: A value or specification which defines a characteristic of asystem, module, apparatus, process, signal or waveform. Parameters maychange.

Parsing: The act of dividing, sub dividing, distributing orpartitioning.

Partial: Less than the whole.

Partitions: Boundaries within phase space that enclose points, lines,areas and volumes. They may possess physical or abstract description,and relate to physical or abstract quantities. Partitions may overlapone or more other partitions. Partitions may be described using scalars,vectors, tensors, real or imaginary numbers along with boundaryconstraints. Partitioning is the act of creating partitions.

Pass band: Range of frequencies with a substantially defined range orchannel not possessing DC response or zero Hz frequency content.

Patches: A geometrical structure used as a building block to approximatea surface rendering from one or more patches.

PDF or Probability Distribution: Probability Distribution Function is amathematical function relating a value from a probability space toanother space characterized by random variables.

pdf or Probability Density: Probability Density Function is theprobability that a random variable or joint random variables possessversus their argument values. The pdf may be normalized so that theaccumulated values of the probability space possesses a measure of theCDF.

Phase Space: A conceptual space that may be composed of real physicaldimensions as well as abstract mathematical dimensions, and described bythe language and methods of physics, probability theory and geometry. Ingeneral, the phase space contemplates the state of matter within thephase space boundary, including the momentum and position for materialof the apparatus.

Plane: Two dimensional geometrical object which, is defined by twostraight lines.

Point: One dimensional mathematical or geometrical object, a singlecoordinate of a coordinate system.

Portion: Less than or equal to the whole.

Possess: To have, or to exhibit the traits of what is possessed.

Power Differential: Comparison of a power level to a reference powerlevel by calculating the difference between the two.

Power Function: Energy function per unit time or the partial derivativeof an energy function with respect to time. If the function is averagedit is an average power. If the function is not averaged it may bereferred to as an instantaneous power. It has units of energy per unittime and so each coordinate of a power function has an associated energywhich occurs at an associated time. A power function does not alter orchange the units of its time distributed resource (i.e. energy inJoules).

Power Level: A quantity with the metric of Joules per second.

Power Source or Sources: An energy source or sources which is/aredescribed by a power function or power functions. It may possess asingle voltage and/or current or multiple voltages and/or currentsdeliverable to an apparatus or a load. A power source may also bereferred to as power supply.

Probability: Frequency of occurrence for some event or events which maybe measured or predicted from some inferred statistic.

Processing: The execution of a set of operations to implement a processor procedure.

Processing Paths: Sequential flow of functions, modules, and operationsin an apparatus, algorithm, or system to implement a process orprocedure.

Provide: Make available, to prepare.

Pseudo-Phase Space: A representation of phase space or application phasespace which utilizes variables common to the definition of the apparatussuch as voltage, current, signal, complex signal, amplitude, phase,frequency, etc. These variables are used to construct a mathematicalspace related to the phase space. That is, there is a knowncorrespondence in change for the pseudo-phase space for a change inphase space and vice versa.

Q Components: Quadrature phase of a complex signal also called thecomplex part of the signal.

Radial Difference: Difference in length along a straight line segment orvector which extends along the radial of a spherical or a cylindricalcoordinate system

Radio Frequency (RF): Typically a rate of oscillation in the range ofabout 3 kHz to 300 GHz, which corresponds to the frequency of radiowaves, and the alternating currents (AC), which carry radio signals. RFusually refers to electrical rather than mechanical oscillations,although mechanical RF systems do exist.

Random: Not deterministic or predictable.

Random Process: An uncountable, infinite, time ordered continuum ofstatistically independent random variables. A random process may also beapproximated as a maximally dense time ordered continuum ofsubstantially statistically independent random variables.

Random Variable: Variable quantity which is non-deterministic, or atleast partially so, but may be statistically characterized. Randomvariables may be real or complex quantities.

Range: A set of values or coordinates from some mathematical spacespecified by a minimum and a maximum for the set

Rate: Frequency of an event or action.

Real Component: The real portion/component of a complex number sometimesassociated with the in-phase or real portion/component of a signal,current or voltage. Sometimes associated with the resistanceportion/component of an impedance.

Related: Pertaining to, associated with.

Reconstituted: A desired result formed from one or more than oneoperation and multiple contributing portions.

Relaxation Time: A time interval for a process to achieve a relativelystable state or a relative equilibrium compared to some reference eventor variable state reference process. For instance a mug of coffee heatedin a microwave eventually cools down to assume a temperature nearlyequal to its surroundings. This cooling time is a relaxation timedifferentiating the heated state of the coffee and the relatively coolstate of the coffee?

Rendered: Synthesized, generated or constructed or the result of aprocess, procedure, algorithm or function.

Rendered Signal: A signal which has been generated as an intermediateresult or a final result depending on context. For instance, a desiredfinal RF modulated output can be referred to as a rendered signal.

Rendering Bandwidth: Bandwidth available for generating a signal orwaveform.

Rendering Parameters: Parameters which enable the rendering process orprocedure.

Representation: A characterization or description for an object, orentity. This may be for example, a mathematical characterization,graphical representation, model, . . . etc.

Rotational Energy: Kinetic energy associated with circular or sphericalmotions.

Response: Reaction to an action or stimulus.

Sample: An acquired quantity or value. A generated quantity or value.

Sample Functions: Set of functions which consist of arguments to bemeasured or analyzed or evaluated. For instance, multiple segments of awaveform or signal could be acquired or generated (“sampled”) and theaverage, power, or correlation to some other waveform, estimated fromthe sample functions.

Sample Regions: Distinct spans, areas, or volumes of mathematical spaceswhich can contain, represent and accommodate a coordinate system forlocating and quantifying the metrics for samples contained within theregion.

Scalar Partition: Any partition consisting of scalar values.

Set: A collection, an aggregate, a class, or a family of any objects.

Signal: An example of an information bearing function of time, alsoreferred to as information bearing energetic function of time and spacethat enables communication.

Signal Constellation: Set or pattern of signal coordinates in thecomplex plane with values determined from a_(I)(t) and a_(Q)(t) andplotted graphically with a_(I)(t) versus a_(Q)(t) or vice versa. It mayalso apply to a set or pattern of coordinates within a phase space.a_(I)(t) and a_(Q)(t) are in phase and quadrature phase signalamplitudes respectively. a_(I)(t) and a_(Q)(t) are functions of timeobtained from the complex envelope representation for a signal.

Signal Efficiency: Thermodynamic efficiency of a system accounting onlyfor the desired output average signal power divided by the total inputpower to the system on the average.

Signal Ensemble: Set of signals or set of signal samples or set ofsignal sample functions.

Signal Envelope Magnitude: This quantity is obtained from (a_(I) ²+a_(Q)²)^(1/2) where a_(I) is the in phase component of a complex signal anda_(Q) is the quadrature phase component of a complex signal. a_(I) anda_(Q) may be functions of time.

Signal of Interest: Desired signal. Signal which is the targeted resultof some operation, function, module or algorithm.

Signal Phase: The angle of a complex signal or phase portion ofa(t)e^(−jω) ^(c) ^(t+φ) where φ can be obtained from

$\varphi = {({sign})\mspace{11mu} \tan^{- 1}\frac{a_{Q}}{a_{I}}}$

and the sign function is determined from the signs of a_(Q), a_(I) toaccount for the repetition of modulo tan a_(Q)/a_(I).

a_(I)(t) and a_(Q)(t) are in phase and quadrature phase signalamplitudes respectively. a_(I)(t) and a_(Q)(t) are functions of timeobtained from the complex envelope representation for a signal.

Signal Partition: A signal or signals may be allocated to separatedomains of a FLUTTER™ processing algorithm. Within a domain a signal maypossess one or more partitions. The signal partitions are distinctranges of amplitude, phase, frequency and/or encoded waveforminformation. The signal partitions are distinguishable by some number ofup to and including v degrees of freedom they associate with where thatnumber is less than or equal to the number of degrees of freedom for adomain or domains to which a signal partition belongs.

Sources: Origination of some quantity such as information, power,energy, voltage or current.

Space: A region characterized by span or volume which may be assignedone or more dimensional attributes. Space may be a physical ormathematical construct or representation. Space possesses a quality ofdimension or dimensions with associated number lines or indexingstrategies suitable for locating objects assigned to the space theirrelative positions as well as providing a metric for obtainingcharacteristics of the assigned objects. Space may be otherwise definedby an extent of continuous or discrete coordinates which may beaccessed. Space may be homogeneous or nonhomogeneous. A nonhomogeneousspace has continuous and discrete coordinate regions or properties forcalculations of metrics within the space which change from some domainor region within the space to another domain or region within the space.A homogeneous space possesses either a continuum of coordinates or adiscrete set of coordinates and the rules for calculating metrics do notchange as a function of location within the space. Space may possess oneor more than one dimension.

Spawn: Create, generate, synthesize.

Spectral Distribution: Statistical characterization of a power spectraldensity.

Spurious Energy: Energy distributed in unwanted degrees of freedom whichmay be unstable, unpredictable, etc.

Statistic: A measure calculated from sample functions of a randomvariable.

Statistical Dependence: The degree to which the values of randomvariables depend on one another or provide information concerning theirrespective values.

Statistical Parameter: Quantity which affects or perhaps biases a randomvariable and therefore its statistic.

Statistical Partition: Any partition with mathematical values orstructures, i.e., scalars, vectors, tensors, etc., characterizedstatistically.

Stimulus: An input for a system or apparatus which elicits a response bythe system or apparatus.

Storage Module: A module which may store information, data, or samplevalues for future use or processing.

Subset: A portion of a set. A portion of a set of objects.

Sub-Surfaces: A portion of a larger surface.

Sub-system: A portion of a system at a lower level of hierarchy comparedto a system.

Subordinate: A lower ranking of hierarchy or dependent on a higherpriority process, module, function or operation.

Substantially: An amount or quantity which reflects acceptableapproximation to some limit.

Suitable: Acceptable, desirable, compliant to some requirement,specification, or standard.

Superposition: A principle which may be given a mathematical and systemsformulation. For n given inputs (x₁, x₂, . . . x_(n)) to a system theoutput y of the system may be obtained from either of the followingequations if the principle of superposition holds; ℑ{x₁+x₂+ . . .x_(n)}=y or ℑ{x₁}+ℑ{x₂}+ . . . ℑ{x_(n)}=y

That is, the function ℑ{ } may be applied to the sum of one or moreinputs or to each input separately then summed to obtain an equivalentresult in either case. When this condition holds then the operationdescribed by ℑ{ }, for instance a system description or an equation, isalso said to be linear.

Switch or Switched: A discrete change in a values and/or processingpath, depending on context. A change of functions may also beaccomplished by switching between functions.

Symbol: A segment of a signal (analog or digital), usually associatedwith some minimum integer information assignment in bits, or nats.

System Response: A causal reaction of a system to a stimulus.

Tensor: A mathematical object formed from vectors and arrays of values.Tensors are geometric objects that describe linear relations betweenvectors, scalars, and other tensors. Elementary examples of suchrelations include the dot product, the cross product and linear maps.Vectors and scalars themselves are also tensors. A tensor can berepresented as a multi-dimensional array of numerical values

Tensor Partition: Any partition-qualified or characterized by tensors.

Thermal Characteristics: The description or manner in which heatdistributes in the various degrees of freedom for an apparatus.

Thermodynamic Efficiency: Usually represented by the symbol η or {tildeover (η)} and may be accounted for by application of the 1^(st) and2^(nd) Laws of Thermodynamics.

$\eta \equiv \frac{P_{out}}{P_{in}}$

where P_(out) is the power in a proper signal intended for thecommunication sink, load or channel. P_(in) is measured as the powersupplied to the communications apparatus while performing it's function.Likewise, E_(out) corresponds to the proper energy out of an apparatusintended for communication sink, load or channel, while E_(in) is theenergy supplied to the apparatus.

$\eta \equiv \frac{E_{out}}{E_{in}}$

Thermodynamic Entropy: A probability measure for the distribution ofenergy amongst one or more degrees of freedom for a system. The greatestentropy for a system occurs at equilibrium by definition. It is oftenrepresented with the symbol S. Equilibrium is determined when

$\left. \frac{S_{tot}}{t}\rightarrow 0. \right.$

“→” in this case means “tends toward the value of”.

Thermodynamic Entropy Flux: A concept related to the study of transitoryand non-equilibrium thermodynamics. In this theory entropy may evolveaccording to probabilities associated with random processes ordeterministic processes based on certain system gradients. After a longperiod, usually referred to as the relaxation time, the entropy fluxdissipates and the final system entropy becomes the approximateequilibrium entropy of classical thermodynamics, or classicalstatistical physics.

Thermodynamics: A physical science that accounts for variables of stateassociated with the interaction of energy and matter. It encompasses abody of knowledge based on 4 fundamental laws that explain thetransformation, distribution and transport of energy in a generalmanner.

Transformation: Changing from one form to another.

Transition: Changing between states or conditions.

Translational Energy: Kinetic energy associated with motion along a pathor trajectory.

Uncertainty: Lack of knowledge or a metric represented by H(x), alsoShannon's uncertainty.

Undesired Degree of Freedom: A subset of degrees of freedom that giverise to system inefficiencies such as energy loss or thenon-conservation of energy and/or information loss and non-conservationof information with respect to a defined system boundary. Loss refers toenergy that is unusable for its original targeted purpose.

Unexcited State: A state that is not excited compared to some relativenorm defining excited. A state that is unexcited is evidence that thestate is not stimulated. An indication that a physical state isunexcited is the lack of a quantity of energy in that state compared tosome threshold value.

Utilize: Make use of

Variable: A representation of a quantity that may change.

Variable Energy Source: An energy source which may change values, withor without the assist of auxiliary functions, in a discrete orcontinuous or hybrid manner.

Variable Power Supply: A power source which may change values, with orwithout the assist of auxiliary functions, in a discrete or continuousor hybrid manner.

Variance: In probability theory and statistics, variance measures howfar a set of numbers is spread out. A variance of zero indicates thatone or more of the values are identical. Variance is alwaysnon-negative: a small variance indicates that the data points tend to bevery close to the mean (expected value) and hence to each other, while ahigh variance indicates that the data points are very spread out aroundthe mean and from each other.

The variance of a random variable X is its second central moment, theexpected value of the squared deviation from the mean μ=E[X]:

Var(X)=E[(X−μ)²].

This definition encompasses random variables that are discrete,continuous, neither, or mixed. The variance can also be thought of asthe covariance of a random variable with itself:

Var(X)=Cov(X,X).

The variance is also equivalent to the second cumulant of theprobability distribution for X. The variance is typically designated asVar(x), ^(σ) ² x, or simply σ² (pronounced “sigma squared”). Theexpression for the variance can be expanded:

$\begin{matrix}{{{Var}(X)} = {E\;\left\lbrack \left( {X - {E\lbrack X\rbrack}} \right)^{2} \right\rbrack}} \\{= {E\;\left\lbrack {X^{2} - {2X\mspace{11mu} {E\lbrack X\rbrack}} + \left( {E\lbrack X\rbrack} \right)^{2}} \right\rbrack}} \\{= {{E\;\left\lbrack X^{2} \right\rbrack} - {2\; {E\lbrack X\rbrack}\mspace{11mu} {E\lbrack X\rbrack}} + \left( {E\lbrack X\rbrack} \right)^{2}}} \\{= {{E\;\left\lbrack X^{2} \right\rbrack} - \left( {E\lbrack X\rbrack} \right)^{2}}}\end{matrix}$

A mnemonic for the above expression is “mean of square minus square ofmean”.

If the random variable X is continuous with probability density functionƒ(x), then the variance is given by;

Var(X)=σ²=∫(x−μ)² f(x)dx=∫x ² f(x)dx−μ ²

where μ is the expected value,

μ=∫xf(x)dx

and where the integrals are definite integrals taken for x ranging overthe range of the random variable X.

Vector Partition: Any partition consisting of or characterized by vectorvalues.

Vibrational Energy: Kinetic energy contained in the motions of matterwhich rhythmically or randomly vary about some reference origin of acoordinate system.

Voltage: Electrical potential difference, electric tension or electricpressure (measured in units of electric potential: volts, or joules percoulomb) is the electric potential difference between two points, or thedifference in electric potential energy of a unit charge transportedbetween two points. Voltage is equal to the work done per unit chargeagainst a static electric field to move the charge between two points inspace. A voltage may represent either a source of energy (electromotiveforce), or lost, used, or stored energy (potential drop). Usually avoltage is measured with respect to some reference point or node in asystem referred to a system reference voltage or commonly a groundpotential. In many systems a ground potential is zero volts though thisis not necessarily required.

Voltage Domain: A domain possessing functions of voltage.

Voltage Domain Differential: Differences between voltages within adomain.

Waveform Efficiency: This efficiency is calculated from the averagewaveform output power of an apparatus divided by its averaged waveforminput power.

Work: Energy exchanged between the apparatus and its communicationssink, load, or channel as well as its environment, and between functionsand modules internal to the apparatus. The energy is exchanged by themotions of charges, molecules, atoms, virtual particles and throughelectromagnetic fields as well as gradients of temperature. The units ofwork may be Joules. The evidence of work is measured by a change inenergy.

: A symbol (typically 3 dots or more) used occasionally in equations,drawings and text to indicate an extension of a list of items, symbols,functions, objects, values, etc. . . . as required by the context. Forexample the notation v₁, v₂ . . . v_(n) indicates the variable v₁, thevariable v₂, and all variables up to and including v_(n), where n is asuitable integer appropriate for the context. The sequence of dots mayalso appear in other orientations such as vertical column or semicircleconfiguration.

v+i: This is the total of the number of desirable degrees of freedom ofa FLUTTER™ based system also known as the blended control Span, composedof some distinct number of degrees of freedom v and some number ofenergy partitions i. v and i are suitable integer values.

v_(i): v_(i) is the i^(th) subset of v degrees of freedom. Each v₁, v₂,. . . v_(i) of the set may represent a unique number and combination ofthe v distinct degrees of freedom. The subscript i indicates anassociation with the i^(th) energy partition. v_(i) is sometimesutilized as a subscript for FLUTTER™ system variables and/or blendedcontrol functions

v,i: This represents a joint set of values which may be assigned orincremented as required depending on context. The set values v, i aretypically utilized as an index for blended control enumeration. Forexample {tilde over (ℑ)}{H(x)_(v,i)} has the meaning; The v^(th), i^(th)function of system information entropy H(x), or some subset of thesefunctions. H(x)_(v,i) may represent some portion of the system entropyH(x) depending on the values assumed by v, i.

x→y: The arrow (→) between two representative symbols or variables meansthat the value on the left approaches the value on the right, forinstance, x→y means x becomes a value substantially the same as y or thevariable x is approximately the same as y. In addition, x and y can beequations or logical relationships.

{tilde over (ℑ)}{H(x)_(v,i)}: This notation is generally associated withblended controls. It has several related meanings including;

a) A function of the v^(th), i^(th) Information Entropy Function parsedfrom H(x)b) A subset of blended controls for which v, i may assume appropriateinteger values.c) An expanded set in matrix form

$\overset{\sim}{}{\begin{matrix}{H(x)}_{1,1,} & {{H(x)}_{1,2}\ldots} & {H(x)}_{1,i} \\\vdots & \ddots & \; \\{H(x)}_{v,1,} & {{H(x)}_{v,2}\ldots} & {H(x)}_{v,i}\end{matrix}}$

The meaning of {tilde over (ℑ)}{H(x)_(v,i)} from the definitions a), b),c) depends on the context of discussion.

+ or +/−: The value or symbol or variable following this ± may assumepositive or negative values. For instance, +/−V_(s) means that V_(s) maybe positive or negative.

+ or −/+: The value or symbol or variable following this + may assumenegative or positive values. For instance, −/+V_(s) means that V_(s) maybe negative or positive.

∫_(H) ^(ul)f(x)dx: Integration is a mathematical operation based on thecalculus of Newton and Leibnitz which obtains a value for the area of acurve under the function of variable x, f(x) between the function limitsof ll a lower limit value and ul the upper limit value.

Σ_(n)x_(n): Summation is a mathematical operation which sums togetherall x_(n)=x₁, x₂, . . . of a set of values over the index n which maytake on integer values.

: The brackets indicate a time domain average of the quantity enclosedby the bracket.

Embodiments of the present invention are directed to modulation(including RF modulation) as well as information encoding architecturesand include allocating resources of the architecture to optimize variousforms of power efficiency including thermodynamic efficiency whileoptimizing the conservation of information transfer through (FLUTTER™).This architecture can be described as FLUTTER™ (FLUTTER™ is a registeredtrademark of ParkerVision Inc., Jacksonville, Fla.) which is a termapplied to an algorithm which controls fluctuation of one or more energypartitions and any number of signal parameters and/or partitions withina transmitter or modulator device to render an information bearingfunction of time in an optimally efficient manner based on availableapparatus resources. For instance, a variable power supply is an exampleof an agile energy partition. One such class of power supplies may be aswitching power supply, which converts variable charge increments perunit time to a specified voltage by using an impedance and anappropriate filter. Such a supply may also distribute charge to a loadwhere variable potentials may be generated.

FLUTTER™ is a distributed modulation algorithm that enables thesynthesis of communications signals at specified output powers andfrequencies with optimized efficiency. The input interface can be anycollection of information samples or suitable continuous informationstreams. The input information possesses entropy H(x) which may bemeasured in bits or bits/second. Both discrete and continuousinformation entropy metrics H(x) may be accommodated. The apparatus mayencode information onto the transmitted signal so as to possess multipledegrees of freedom that are excited by parallel domains of information{tilde over (ℑ)}{H(x)_(v,i)} which are constructed from the sourceentropy H(x). v is a number of degrees of freedom usually associatedwith a modulator or encoder and i (also degrees of freedom) is a numberof partitions usually associated with one or more power sources for themodulator or encoder. H(x)_(v,i) may also be represented as H_(x) _(v,i),

H_(x_(v_(i))),

or H(x)_(v) _(i) depending on the context and organization ofdistributed blended controls. These shorthand notations are related toone another through the counting indices of suitable integer values, v,i. The random variable x is an argument from a probability densityfunction used to characterize the stochastic nature of the samples fromthe information process. {tilde over (ℑ)}{H(x)_(v,i)} is a function withinput H(x) and multiple outputs generated from the function ofH(x)_(v,i). FIG. 1 illustrates a high level operational flow 100 of theFLUTTER™ algorithm (module) 130 along with the analog and compositingsegment (module) 131 of the transmitter.

The set {tilde over (ℑ)}{H(x)_(v,i)} may partially share domains whichare dependent through statistical correlations determined from H(x) 101and the characteristics of the compositing and/or Multiple Input SingleOutput (MISO) and/or

operator 131 segment (module). Therefore, the relative prominence orweighting of the {tilde over (ℑ)}{H(x)_(v,i)} blended controls aredynamically variable according to the FLUTTER™ algorithm. The blendedcontrols {tilde over (ℑ)}{H(x)_(v,i)} may be realized as sampledfunctions and/or continuous signals generated and distributed by the(VSE) vector synthesis engine (module) 130. Furthermore, the sampledrate of any member of the set of blended controls may be less than theminimum Nyquist sampling rate associated with a final output signal,120, providing certain signal processing advantages without sacrificingsignal quality or losing information in the modulation process. Thebandwidths and power spectral densities associated with each of theblended controls 102 may be unique.

The compositing and/or MISO and/or

operator (module) 131 operations integrate and statistically adjustparallel processing paths, which may be nonlinear. The nonlinearity,when present, extends through the FLUTTER™ algorithm and blendedcontrols, analog compositing and/or MISO operations. FLUTTER™ refers tothe statistical parsing of information to each blended control from theset {tilde over (ℑ)}{H(x)_(v,i)} in a manner which excites the multipledegrees of freedom in the apparatus to form the final desired signal inthe most efficient manner to conserve power, conserve information andreduce thermal footprint.

The nature of the algorithm 100 is feed forward and does not requirefeedback. Circuits forming the analog paths are not required to belinear although the final output 120 represents a desired signal withminimal ACPR, harmonics, noise and other artifacts usually associatedwith nonlinear operations on signals.

Accordingly, it is an embodiment of the present invention to utilize oneor more novel power source(s), which may be described as a digitallycontrolled power source (DCPS), which may be, for example, unipolar, orbipolar. These novel power source(s) may be described in terms of adigitally controlled switching power supply that is adjustable over arange of values from, for example, approximately 0 volts to V_(s) volts,or −V_(s) to +V_(s) volts, accommodating maximum and minimum chargetransfer at a voltage (for any corresponding load) which may have arelatively low source impedance Z_(s) for the frequency range ofinterest. Low impedance in this case means, R_(s), the real portion ofZ_(s), is low compared to the load that is attached to the DCPS. Thelowest possible “real” portion of the source impedance Z_(s) is usuallydesired. The novel power sources, according to one or more embodimentsof the present invention, provides an alternative, providing efficient“on the fly” signal envelope reconstruction, for RF modulators. As datarates and peak to average power ratios (PAPR) increase for signalingstandards, the switching power supply becomes more difficult to designif it is used to track the envelope for a waveform during the modulationprocess. This issue is due, in part, to the rate of change of chargetransfer allocated to follow the signal envelope with a specifiedprecision under significant load. The envelope reconstruction in amodern standards based application must be nearly exact.

Switching power supplies generate significant distortion over portionsof the output dynamic range and also sacrifice some efficiency.Therefore, it is difficult for envelope restoration or envelope trackingbased modulators to effectively reconstruct signal envelopes usingswitching supplies over the full dynamic range without utilizingfeedback loops. Embodiments of the present invention are directed toarchitectures and algorithms that can be open loop feed forward schemes(OLFF). Thus, embodiments of the present invention offer a solution to aLegacy challenge in the DCPS switching art.

For example, FLUTTER™ may be used to facilitate practical DCPS design,diverting resources to other degrees of freedom to reconstruct theinformation bearing function of time, which may be, for example, awaveform, or signal. Manipulation of the energy partition over aspecified dynamic range in concert with additional modulator degrees offreedom enhances efficiency and preserves waveform quality. Thetechniques described in relation to the DCPS may also be used with othersuitable switching power supply and energy source technologies as well.FLUTTER™ algorithms control the DCPS by assigning optimal transitionstates and voltage or current amplitudes at specifically designedinstants of time given a fixed number of power source levels and thedesired signal statistic. Optimization is determined as a maximizationof thermodynamic Efficiency vs. Signal/Waveform quality.

A modulation device suitable for use with FLUTTER™, may be, for example,an RF power modulation apparatus capable of implementing standards basedcommunications, yet possessing appropriate degrees of freedom wheneverthe tradeoff between information capacity and power efficiency andsignal quality is a driving concern. It is usually desirable for themodulator to possess more degrees of freedom than legacy modulatorarchitectures reflecting current state of the art.

FIG. 2 shows a block diagram 200 that illustrates a modulator, such as,for example a d2p™ apparatus, 214, power source, or energy source 208and local oscillator 210.

FIG. 2 illustrates a set of controls 202 referred to herein as a blendedcontrol function, {tilde over (ℑ)}{H(x)_(1,i), H(x)_(2,i), . . .H(x)_(v,i)}. {tilde over (ℑ)}{H(x)_(1,i)}, and {tilde over(ℑ)}{H(x)_(2,i)}, shown as 202(a) and 202(b), respectively, are two ofthe set of controls 202 that manipulate degrees of freedom for theenergy and entropy conversion functions 215, power source 208 and localoscillator (LO) 210, respectively. Degrees of freedom may include, forexample, undesired degrees of freedom and desired degrees of freedom.The undesired degrees of freedom, scavenge power from the system 200.The scavenged power is wasted and therefore is not available to supportthe intended apparatus function and dissipates as unwanted heat.Undesired degrees of freedom include degrees of freedom that are notdeliberately designed into the system 200. The desired degrees offreedom are information bearing and include degrees of freedom that aredeliberately designed as part of the system 200. Typically, the desireddegrees of freedom are excited or stimulated and the response orreaction of the undesired degrees of freedom is minimized by theFLUTTER™ algorithms, with respect to the degrees of freedom, v_((tot)):

v_((tot))=total number of degrees of freedom. v_((tot)) includes desireddegrees of freedom as well as undesired degrees of freedom. i=subset ofdesired degrees of freedom and may also be referred to as a number ofenergy partitions. Domains are distinguished by, for example, one ormore deliberate groupings from the joint set or subsets of v, i where v,i are suitable integers with a span of v+i. The indices v, i enablemathematical accounting associated with operations and functions of thedomains.

It is an embodiment of the present invention to minimize the reaction ofthe undesired degrees of freedom to an excitation or stimulation of thedesired degrees of freedom. The response to the excitation of thedesired degrees of freedom is a known quantity, since the apparatus, orsystem is programmed for a desired response based on inputs. Theapparatus or system may be characterized to obtain parameters, constantsand variables associated with the system which become collectively priorknowledge and from a random processes perspective apriori information orknowledge. An embodiment of the present invention, for example thesystem 200 minimizes the probability of exciting undesired degrees offreedom by maximizing the information rate subject to minimized averagedpower and constraining quality metric for the output signal 220 throughresource allocation to the desired degrees of freedom. Embodiments ofthe present invention also monitor/analyze the response of the desireddegrees of freedom and the undesired degrees of freedom. Theoptimization technique allocates resources to desired degrees of freedomto minimize influence of the undesired degrees of freedom, given thegoals of efficiency and signal quality.

The overall purpose for blended controls {tilde over (ℑ)}{H(x)_(1,i),H(x)_(2,i), . . . H(x)_(v,i)} 202 is to manipulate degrees of freedomfor the modulator apparatus 214 in such a manner to maximize η thethermodynamic efficiency of the modulator apparatus 214 while minimizingunwanted degrees of freedom and constraining the modulator apparatus 214according to a function of a specified information metric H(x), (seeFIG. 3 element 309) known as Shannon's Information Entropy. Minimizingthe unwanted, or undesired, degrees of freedom controls the probabilitythat the undesired degrees of freedom will be excited when energy isapplied to the system, in accordance with information encoding andmodulation.

Proper thermodynamic efficiency is defined consistent with the 1^(st)Law of Thermodynamics and given by;

${\langle\eta\rangle} = {\frac{\langle{\overset{\_}{P}}_{out}\rangle}{\langle P_{in}\rangle} = \frac{\langle E_{out}\rangle}{\langle E_{s_{in}}\rangle}}$

-   P _(out)    Δ Time Averaged power of output contained by the signal of interest    only, this excludes noise, ACPR, harmonics, spurious, etc. according    to a standard's-based metric.-   P_(in)    Δ Time Averaged power of input provided by one or more power sources    such as a battery, for example.-   E_(out)    Δ Time Averaged output energy for the signal of interest.-   E_(s) _(in)    Δ Time Averaged input energy from sources, also labeled as E_(s).

While FIG. 2 illustrates the LO (local oscillator) 210 and power source,E_(s), 208 separate from the modulator apparatus 214, which may be, forexample, a d2p™ modulator apparatus, this is only one embodiment.Architectures, which include the LO synthesizer 210 and an agile E_(s),208 as well as partitions that completely exclude their control are alsoembodiments of the present invention and may be considered as part ofthe algorithm options and technology. Also shown in FIG. 2 is P_(in)212, P_(out) 216 and output signal 220. Energy and entropy conversionunit 215 receives input with power P_(in). 212 from E_(s) 208 and inputfrom LO synthesizer 210. The power or energy source 208 may be any A.C.or D.C. current or voltage source or combination thereof. The associatedcharacterization pdf for the source may possess stochastic anddeterministic attributes. The energy and entropy conversion unit 215generates output signal 220, according to a portion of the blendedcontrol input 202. Each of the blended controls (202) from subsets ofcombinations and permutations of v·i indices, may be realized bymultiple signals per control path. For instance {tilde over(ℑ)}{H(x)_(z,i)} may be instantiated using multiple signals. The signalsmay be digital, analog, serial, parallel or multiplexed with one or morethan one connecting structure such as a wire or bus and a suitablenumber of connecting nodes.

In one embodiment of the present invention, architectures whichcontemplate “on the fly” control of the system energy source, E_(s), 208as one of several degrees of freedom are described. Control of E_(s) 208over some portion of the dynamic range of signal envelope along with anynumber of other signal parameters, is one embodiment of FLUTTER™.

FIG. 3 shows an architecture 300 that illustrates an example usingoptimization parameters. FIG. 3 shows one example of a model that may beadapted to multiple applications that are appropriate for analyzingcommunication's systems to determine thermodynamic quantities.

As shown in FIG. 3, energy partitions 324(a) . . . (n) (where “n” is anysuitable number) from the source E_(s) 308 are weighted and transformedaccording to the associated λ_(v) _(i) 326 (a) . . . (n) (where “n” isany suitable number) and

operators to produce a result, as shown in block 319. In thiscircumstance the subscript v_(i) pertains to the i^(th) subset from vdegrees of freedom. Each v_(i) forms a domain for degrees of freedomassociated with i partitions where v, i are suitable integers which mayvary. v may vary for each i. Also sets of degrees of freedom up to andincluding v degrees of freedom may associate with each value of i. “

” operators are a class of mathematical and logical operations whichoptimize the compositing step in a FLUTTER™ algorithm according to ablended control. The blended controls 330, 332 and 334 are derived from{tilde over (ℑ)}{H(x)_(v,i)} 309. The thermodynamic entropy flux, S_(J),350 as well as E_(e) _(out) 352, gives rise to signals and signalenergy, which are referred to as essential signals and essential energy.Energy 321, shown as essential energy, as well as unwanted phenomena 322such as heat, ACPR, inter modulation distortion (IMD) Harmonics,quantization noise, thermal noise, radiation, and/or other waste energy,is also partially stimulated as a function of {tilde over(ℑ)}{H(x)_(v,i)} 309. FIG. 3 does not explicitly illustrate the specificentropy flow; however, it is implied since the input includes Shannon'smetric for information entropy. Information entropy and apriori systemknowledge is used as a prescription or instruction for developingblended control which motivate or stimulate or excite the variousphysical degrees of freedom within the apparatus, in turn generating acorresponding causal rise to thermodynamic entropy flux S_(J) 350 whichis manifest as a perturbation of the variables within the system phasespace. This process is coupled to a modulator apparatus that generatesthe output signal constellation 318. FIG. 3 is useful to follow theoptimization theory, and the description below provides expressions forEnergy and Entropy flux. Energy and Entropy flux are functions of timecoordinates in addition to the indices v, i. The expanded equationsillustrate the dependency on time with the time sample t_(k) where k=0,1, 2, 3 . . . .

${E_{e_{out}}\left( t_{k} \right)} = {\sum\limits_{v}{\sum\limits_{i}\left\lbrack {\lambda_{v_{i}}\eta_{v_{i}}E_{S_{v_{i}}}} \right\rbrack_{(t_{k})}}}$${E_{w_{out}}\left( t_{k} \right)} = {\sum\limits_{v}{\sum\limits_{i}\left\lbrack {{\lambda_{v_{i}}\left( {\eta_{v_{i}} - 1} \right)}E_{S_{v_{i}}}} \right\rbrack_{(t_{k})}}}$${S_{J_{tot}}\left( t_{k} \right)} = {\sum\limits_{v}{\sum\limits_{i}\left\lbrack {O_{v,i}\left\{ E_{S_{v_{i}}} \right\}} \right\rbrack_{(t_{k})}}}$

Additional variable definitions generally apply to the model and will beemployed herein.

${\eta \left( t_{k} \right)} = \left( \frac{E_{e_{out}}}{E_{e_{out}} + E_{w_{out}}} \right)_{(t_{k})}$E_(s_(in)) = E_(e_(out)) + E_(w_(out))

-   E_(s) _(in)    System Input Energy-   E_(e) _(out)    Effective System Output Energy-   E_(w) _(out)    A Waste System Output Energy-   η_(t) _(k)    Efficiency as a Function of the Time at Sample k

v pertains to the macroscopic partition of the information sourcedomains {tilde over (ℑ)}{H_(v) ₁ , H_(v) ₂ , . . . H_(v) _(i) }. (i)accounts for the macroscopic energy partitions which are also dependenton H(x) as a function {tilde over (ℑ)}{H_(x) _(v,i) } (shown in FIG. 3as element 309). The assignment of energy partitions to informationdomains is flexible and depends on particular design considerations.

H(x) or alternatively, H (p(x)) is known as Shannon's informationentropy, uncertainty or measure of information or information metric.These may be referred to herein by the shorthand notations H(x) andH_(x). Also the information metric may be enumerated according toH(x)_(v,i) or

H_(x_(v_(i)))

or H_(x) _(v,i) or H_(v) _(i) where v and i are integers correspondingto degrees of freedom and partitions. Subsets of index values (v, i) canbe used to define domains. Each of the i energy partitions may possessany number of degrees of freedom up to and including v. Any subset fromthe v degrees of freedom is permissible. H(x) is given in the discreteand continuous forms;

The metric H(x) may have units of bits or bits/per second depending oncontext but is defined by

${H(x)} = {- {\sum\limits_{l}{p_{l}{\ln \left( {p(x)}_{l} \right)}}}}$

in the case where p(x)_(t) is the pdf of a discrete random variablewhere the index l accounts for the l^(th) probability in the pdf.

If p(x) is a continuous random variable then;

${H(x)} = {- {\int_{- \infty}^{+ \infty}{{p(x)}\ln \frac{p(x)}{m(x)}\ {x}}}}$

With mixed probability densities, composed of mixed random variables,both discrete and continuous entropy functions may apply with anormalized probability space of measure 1. Whenever the logarithm b=2,the information is measured in bits. If b the base=e, then theinformation is given in nats.

p(x) is the probability density functions (pdf) of symbols emitted fromthe information source.

m(x) normalizes Shannon's continuous entropy formulation to avoidconditions of negative entropy.

The functions of interest are obtained from;

The physical restrictions imposed by the apparatus and its environment.

-   a) Mapping of H(x) to the available degrees of freedom of the    apparatus subject to the optimization considerations;

max{η}

min{H(x)−H(y)}

max{S _(J) _(e) −S _(J) _(w) }

-   -   H(x) Δ Information Entropy of the Source    -   H(y) Δ Information Entropy referenced to the Modulated Signal    -   S_(J) _(e) Δ Effective Thermodynamic Entropy Flux    -   S_(J) _(w) Δ Waste Thermodynamic Entropy Flux

The total thermodynamic entropy flux of the system is given by;

S _(J) _(tot) =S _(J) _(e) +S _(J) _(w)

S _(J) _(e) ∝{tilde over (ℑ)}{H(x)}_(t) _(k)

The flux S_(J) _(e) is part of the total entropy flux S_(J) _(tot) andnot in full relaxation with the environment in a thermal sense untilsome period after entropy production ceases. In cases of full relaxationand long observation time constants, t_(eq), the following entropyrelationship applies in a specified irreversible direction, consistentwith the 2^(nd) Law of Thermodynamics.

{tilde over (ℑ)}{H(x)}→S _(e) +S _(w) : t _(eq)→∞

S _(e) +S _(w) ≦S _(tot)

The arrow→ can be interpreted as “tends toward”.

A message duration in time is given by τ. Thus, the total decoding time,which is the time interval to extract information from an encodedsignal, is greater than or equal to message length, which can becomearbitrarily large depending on the required channel capacity. In thisspecific case, channel refers to the modulator apparatus and portions ofsurrounding support circuitry. When the observation time exceeds thedecoding time by a very significant amount in the prior equation, theimplication is that the communication has reached a quasi-static stateand information transfer is terminated during the remainder of t₀−τ,where t₀ is the total observation time.

The entropies S_(e) and S_(w) are equilibrium entropies since theyapproach a maximum, and

$\frac{S_{tot}}{t}->0.$

The implication is mat consumption of H(x) through signal generation andtransport increases environmental entropy, which can be measured forfinite messages if the system is closed. In a perfect system S_(w)→0 andthere would be no heat generated by the apparatus. The only heat wouldappear due to S_(e) in the test load (communication sink), via the testchannel, once the system reaches equilibrium.

This acknowledges that S_(J) _(e) , the essential entropy flux, doesultimately dissipate whenever the communication process is suspended,and that energetic modes associated with transporting H(x) eventuallydegrade to a maximum entropy state, thus preserving the 2^(nd) Law ofThermodynamics.

In this treatment, spontaneous reconstitution of the informationassociated with H(x) from S_(tot) cannot be obtained even iffluctuations in the thermalized environmental entropy occur, after fulldissipation of information. Information is annihilated or channelcapacity diminished as S_(J) _(w) (waste thermodynamic entropy flux)increases and S_(J) _(e) (essential thermodynamic entropy flux)decreases. In this case, reference is made to the term “annihilation” astransfer of information entropy into non information bearing degrees offreedom that are no longer accessible to the information bearing degreesof freedom of the system and therefore “lost” in a practical sense evenif an imprint is transferred to the environment through a correspondingincrease in thermodynamic entropy. Also, the term channel may be anymedium used to transport some portion of information entropy H(x) evenif the channel (medium) is bound to some portion of an apparatus. Noiseprocesses and thermal conduction arising from energy dissipation arecontemplated along with causal perturbations determined by the apparatusresponse to a function of H(x) (shown in FIG. 3 as element 309). Hence,both driving forces and spontaneous actions coexist.

Typically, practical applications demand some consideration of opensystems, which can complicate the definitions for waste and effectiveentropies. In order to explain embodiments of the present invention,waste entropy may be defined as the logarithm of the number ofsignificant accessible states associated with the portions of the phasespace containing undesirable degrees of freedom and their cascadedenergetic modes for the apparatus, multiplied by Boltzmann's constantfor consistency with general thermodynamic treatments. The applicationdensity of states within the phase space consists of functions ofparticle and charge motion, dq/dt, their electromagnetic fields, as wellas undesired molecular thermal agitation, translation, rotation, and/orvibration (molecular kinetic energy), and other kinetic anomalies whichmay be described as undesired degrees of freedom.

Likewise, the effective entropy is derived from the number of accessiblestates attributed to the portion of phase space encompassing thedesirable energetic modes encompassing or enabling desired degrees offreedom. These definitions capture the spirit of a statistical mechanicsdescription without demanding conditions of thermal equilibrium.However, it should also be noted that both forms of entropy (waste andeffective) may assume intermediate flux expressions, which ultimatelywill seek a maximum entropy state when fully absorbed by theenvironment. This dissipation is eventually realized as heat, or otherwaste energy. Nonetheless, system thermal relaxation times may besignificant when compared to intermediate modes of entropic transfer.This fact promotes efficient transport of energy within the multipledegrees of freedom for the apparatus to physically encode information ina form compliant for consumption by an information sink once thecomponent entropies are reintegrated, or composited.

This reintegration or compositing enables functions of the informationdomains (subsets of H(x)_(v,i)) to be used with appropriate statisticalweight, substantially simultaneously (or concurrently or in parallel) torender a representation of an information bearing function of time, suchas a signal, waveform, electronic representation of an informationbearing function of time or a facsimile of an information bearingfunction of time. Statistical parsing associated with a compositingprocedure may also occur sequentially according to a FLUTTER™ algorithm.This compositing may form the representation of the information bearingfunction of time and/or reconstruct an information bearing function oftime and/or render the information bearing function of time, or afacsimile thereof.

Compositing involves combining, mixing and/orunifying/integrating/re-integrating, a collection of signals, into aninformation bearing function of time.

Another embodiment of the present invention is directed to a method forassigning {tilde over (ℑ)}{H(x)_(v,i)} (generally shown in FIG. 3 aselement 309) the weighting of λ_(v) ₁ , λ_(v) ₂ , . . . λ_(v) _(i) ,(generally 326) the partitions of E_(s), (308) (generally 324) and theoptimization process in a modulation system that utilizes FLUTTER™. Thisapproach maximizes efficiency, minimizes waste entropy production andconserves information transfer. Embodiments of the present inventioncontemplate exploiting an advantageous hardware architecture givenpractical technology restrictions, while applying the optimizationcriteria of the FLUTTER™ algorithm.

The description herein uses {v, i} subscripts to account for v distinctdegrees of freedom and i energy partitions. The i energy partitions alsorepresent particular degrees of freedom. Macroscopic degrees of freedommay be defined as the unique portions of application phase space whoseseparable probability densities may be manipulated by unique physicalcontrols derivable from the function or set of functions {tilde over(ℑ)}{H(x)_(v,i)}. This function takes into consideration, or isinfluenced by, desired degrees of freedom and undesired degrees offreedom for the system. These degrees of freedom (undesired and desired)can be a function of system variables, such as temperature, and may becharacterized by prior knowledge of the apparatus/system. The twoindices v, i may include any number of operations, manipulations orprocesses that can be described mathematically or with logic or bothmathematically and with logic. Thus, an overall density of states forthe application phase space is dependent on applicable subsets of v, iprobability distributions. These domain distributions will have varyingdegrees of statistical co-dependence.

As described herein, it is possible to use a less rigorous definitionbetween the available physical controls and the distributions of theresources they affect to expedite a particular example. Typically, at afundamental level, the degree of freedom will possess two attributes: 1)be associated with some portion of the density of states within thephase space; which in turn relate to physical encodingmechanisms/facility of the apparatus and 2) permit articulation ofenergetic functions which are encoded with information, distributedaccording to {tilde over (ℑ)}{H(x)_(v,i)}, where {tilde over(ℑ)}{H(x)_(v,i)} controls the encoding mechanism/facilities of theapparatus.

These two attributes possess correspondence to the random variablesdescribing quantities within the phase space. Thus, these attributes maybe considered when the term “degrees of freedom” is used herein.

FIG. 4 shows an alternate block diagram 400 illustrating the parsing ofH(x) through a control {tilde over (ℑ)}{H(x)_(v,i)} 402. FIG. 4 is aparticular example of a portion of the embodiment of FIG. 3 and showssome examples of additional electronic functions.

FIG. 4 shows that the energy source E_(s) 408 is manipulated by somefunction of a subset {tilde over (ℑ)}{H(x)_(v,i)} of 402(a), derivedfrom the information metric H(x). In addition {tilde over(ℑ)}{H(x)_(v,i)} 402 is related to the control of magnitude and phasefunctions of the carrier wave, where such carrier wave of radianfrequency ω_(c) is obtained from one or more local oscillators (a singlelocal oscillator (LO) 410 is shown). It is also an embodiment of thepresent invention that there may be any suitable number of localoscillators 410. The embodiments contemplated herein may utilizemultiple LOs, such that the number of LOs is based on designconsiderations. ω_(c) may be greater than or equal to zero radians persecond.

Additionally, there may be a plurality of carrier waves.

H(x) 402 is translated to the load encoded in the form of a signal whileminimizing distortions at specified power and maximum efficiency througha large dynamic range for a number of operational variables. Potentialenergy from E_(s) 408 is converted to a desired form, via thetrans-impedance of the multiple input single output module (MISO) 466,as shown by trans-impedance node 462, and transferred directly from thepower source 408 to the output load R_(L) 464 through energy storageelements 467 and complex impedance Z_(m) 469, in charge increments,dq/dt. The algorithm for distribution of {tilde over (ℑ)}{H(x)_(v,i)}(402) is open loop, yet based on prior knowledge concerning the physicalprinciples and characterized parameters of the apparatus 400.

The multiple input single output operator module MISO 466 is implementedby hardware and algorithms, which in aggregate may be associated withthe operators λ_(v) _(i) ,

, referenced in FIG. 3. Degrees of freedom implemented via MISO module466 are assigned in a manner that permits separate and jointmanipulation of composite and other subordinate phase spaces.

The energy flow path 465 through energy storage element 467, which maybe, for example, an inductive element and energy flow path 468 throughelement 469, which is shown as an impedance element, are also shown. Theenergy paths 465 and 468 are used to illustrate that the energy isdisplaced from one point in time and space to a second point in time andspace. The energy storage element and related circuits use space andtime as required to transport charge. Alternately the energy storageelement may be any combination of reactive elements, for instancecapacitors and inductors as well as transmission lines, or resonatorsarranged in any suitable circuit topology. The power or energy source408 may be any A.C., D.C. current or voltage source or combinationthereof. The associated characterizing pdf for the source may possessStochastic and deterministic quantities.

Each of the blended controls 402 from subsets of combinations andpermutations of v, i indicies may be accomplished by distribution ofmultiple signals per control path. For instance path 402(a) may bedigital, analog, serial, parallel or multiplexed with one or more thanone connecting structure such as a wire or bus and suitable number ofconnecting nodes.

The use of phase space herein is expanded from that of StatisticalMechanics. The phase space, as described herein, accommodates theconsideration of both apparatus macroscopic and microscopic degrees offreedom. The expanded definition recognizes joint evolution of thesedomains over variable relaxation times. This definition is consistentwith maximal entropy non-equilibrium statistical characterizations aswell as non-equilibrium thermodynamics.

Traditionally, heat energy is the motivator for classicalthermodynamics. In addition, multiple forms of energy can coexist.Notably, dynamic charge and its electromagnetic field and thermalagitation play roles in electronics though heat is usually not desiredfor most modern forms of communication and therefore is generallyregarded as the degradation of energy to a form possessing maximumentropy. The majority of (1−η)E_(s) may consist of Joule heat, thoughnot exclusively. Intermediate energetic expressions such as noise,harmonics, intermodulation distortion, unwanted oscillations, crosstalk,interference, rotational, vibrational, translational and spuriouswaveforms, represent examples of scavenging phenomena, which decrease nat the point of delivery. Of course, these other forms eventually alsodegrade to the most primitive form, heat, after causing errors such asdistortions and defects in signals.

According to embodiments of the present invention, practical scenarioswill possess a relatively few degrees of freedom (compared to v_(tot))within the portion of the device that articulates charge transfer. Thisis due to considerations for signal management complexity and theassociated 2^(nd) Law of Thermodynamics consequences. Though largequantities of charge can be transported with some undesired variation,there is typically a dominant bulk statistic on a sample-to-samplebasis. Sample in this circumstance may include the numericalquantization of signals. This quantization is typically subject to theNyquist-Shannon sampling criteria and sampling theorems. Relevant unitsare in terms of charge per unit information per sample per unit time.The charge transport may be interpreted in terms of currents, energies,as well as magnitude and phase functions of currents in the case ofcomplex signal spaces. Charge transport may also be given in terms ofvoltage functions given knowledge of system impedances.

According to an embodiment of the present invention, as describedherein, an apparatus phase space contemplates one or more degrees offreedom, which may include macroscopic and microscopic degrees offreedom. Furthermore, the phase space will typically possess transitoryproperties. Both circumstances can include a non-homogeneous phasespace. Statistical properties of constituent phase space domains can beexploited in concert with the diversity of phenomena relaxation timeconstants to decouple otherwise intractable dependencies.Semiconductors, conductors, inductors, and capacitors transport charge,and energy characterized by microscopic and/or macroscopic statistics.However, these infra structures are also composed of matter that issubject to thermal agitation at the microscopic level. When describingefficiency and information transport, to be complete, both regimesshould be addressed, explicitly or implicitly. These extended conceptsof application phase space may be referred to herein as simply “phasespace”.

FIG. 5 show a circuit representation treated as a channel 500. Thiscircuit representation 500 includes a signal source 570 which possessesa describing a pdf p(x) possessing information entropy H_(x) Thevariable x is mapped into voltage V_(src) 572. The signal source 570 hasa source impedance with real part R_(s) 571. The signal V_(src) 572traverses a channel 573. The output of the channel 573 is a load voltageV_(L). 574. The information entropy associated with the load voltage isH_(y) 575 and the signal V_(L). 574 is dissipated by the real part of aload impedance R_(L) 564. Collectively 500 can conceptually representsome portion of an apparatus of system which transports or processes asignal, at a high level of abstraction. The input signal voltage V_(src)572 may be different than V_(L) 574 the output signal voltage becausethe channel 573 may modify the input V_(src) 572 by some nonlineardistortion and/or addition of noise interference. Likewise, the originalmapping of information and its associate entropy H_(x) (see 570) can bemodified by the channel with the loss of information. In thisrepresentation 500 the channel and its distortions represents apparatusimperfections which may be included in the definition of or descriptionof phase space or application phase space or pseudo-phase. Theprobability densities (pdf's) used to describe charge, voltage,information and related functions of those quantities also may bedistorted by the channel 573.

The pdf (probability density function) describes the distribution of aparameter, or quantity, such as voltage or charge of functions thereof,which may be utilized. This is useful since such parameters can berelated to properties of the phase space. Also, their distributions playa significant role in allocating {tilde over (ℑ)}{H(x)_(v,i)}. V·(dq)represents energy where dq plays the extensive role. V can be a complexquantity and therefore provides a minimum of two degrees of freedom insignal space or pseudo-phase space. The pseudo-phase space may be, forexample, an abstract representation or approximation of a portion ofphase space or application phase space. Distortions that impact thephase space and pseudo-phase space may sometimes be corrected, oravoided, by exploiting additional degrees of freedom. Distortions affectthe manner in which information is mapped into voltage and currentwithin the apparatus. Undesirable mappings can annihilate informationand decrease efficiency. By parsing H(x) 570 into multiple constituentsH(x)_(v,i) and mapping functions of the constituents along certaintrajectories of phase space or pseudo-phase space a composite outputderived from said trajectories may conserve information and maximizeefficiency. As discussed in the Background section, this isfundamentally different than pre-distortion technology, which countersthe nonlinearity with an inverse transfer characteristic, which modifiesthe phase or pseudo-phase space in a certain way without considerationof the most efficient phase space or pseudo-phase space trajectories fortransitions between system states. Hereafter, it is understood that theterm phase space may be used to encompass the meanings of pseudo-phasespace or application phase space depending on context.

It is useful to consider some rudimentary aspects of relevant pdfs forsubsequent reference (probability density functions). Consider thesimple one-dimensional case of a pdf (probability density function) forV_(src) to be approximately Gaussian as illustrated in FIG. 6.

Specifically, FIG. 6 shows a graphical representation 600 of anapproximate Gaussian PDF with 0.5 mean. As shown in FIG. 6, V_(src) isplotted on the X-axis (horizontal) 672 and the probability for aspecific value of V_(src), p(V_(src)), is plotted on the Y-axis(vertical) 676. Curve or plot 677 implies a linear channel.

Another embodiment of the present invention is that, for example,suppose an asymmetric nonlinear function is applied to a channel with aGaussian signal which limits values of V_(src) above V_(ε). The Gaussiansignal may have the pdf for V_(src) depicted in FIG. 6 applied to thechannel nonlinearity of FIG. 5.

A pdf (probability density function) is shown in FIG. 7. FIG. 7 shows agraphical representation 700, which shows V_(src) is plotted on theX-axis (horizontal) 772 and p({tilde over (V)}_(src)) is plotted on theY-Axis (vertical) 776. Curve or plot 777 is shown. At point 0.6, asshown by 773 a vertical delta function, the curve 777 is truncated.

{tilde over (V)}_(src) which has a new maximum at the value V_(ε)=0.6773 is the new signal derived from V_(src) after clipping (applicationof nonlinearity of FIG. 5). The asymmetry of p({tilde over (V)}_(src))and the inclusion of an appended delta function account-for thedisplaced probability mass of the original p(V_(src)). With the appendeddelta function, the total probability measure is,

∫_(−∞) ^(∞) p({tilde over (V)} _(src))d{tilde over (V)} _(src)=1

As shown in FIG. 7, the uncertainty for the signal has been removed for{tilde over (V)}_(src)>V_(ε). Likewise, the uncertainty metric H(y) isalso affected because the correspondence between the mapping of H(x) andits component density function p({tilde over (V)}_(src)) plotted onY-axes has been significantly altered. Using Shannon's notation thecapacity will also be modified.

H(x)+H _(x)(y)=H(y)+H _(y)(x)

H(x)−H _(y)(x)=H(y)−H _(x)(y)

R

H(x)−H _(y)(x)

max{R}ΔC

-   H(x): Uncertainty metric or information entropy of the source in    bits (or bits/sec).-   H_(x)(y): Uncertainty of the channel output given precise knowledge    of the channel input.-   H(y): Uncertainty metric for the channel output in bits (bits/s).-   H_(y) (x): Uncertainty of the input given knowledge of the output    observable (this quantity is also called equivocation).-   R: Rate of the signal moving through the channel in bits/sec.-   C: Capacity given H(x), H(y), H_(y) (x), H_(x)(y)

Examination of p({tilde over (V)}_(src)) indicates that V_(src) isambiguous once V_(ε) is exceeded on the input to the channel where V_(ε)is the voltage at which V_(src) clips. That is, H_(y)(x) is increasedfor this case. Hence

H _(y→{tilde over (V)}) _(src) (x)>H _(y→V) _(src) (x)

Therefore;

max{H(x)−H _(y→V) _(src) (x)}>max{H(x)−H _(y→{tilde over (V)}) _(src)(x)}

C _(V) _(src) >C _({tilde over (V)}) _(src) ,

This proof is consistent with Shannon's theorems. The proof supports theinformation loss proposition. It is ascertained that for certain valueranges of V_(ε) that the link can be broken (through information loss)beyond an acceptable limit. A quality metric for assessing thedegradation is given by;

$\frac{C_{{\overset{\_}{V}}_{src}}}{C_{V_{src}}} = {1 - C_{\deg}}$

where C_(deg) represents the percentage channel capacity degradation.C_(deg) may be a useful metric for assessing the information impact ofalgorithm nonlinearities.

Manipulation of the pdf (probability density function) conserves chargeand associated fields related to the physical processes but theuncertainty of the charge functional may be reduced and thereforeShannon's information uncertainty metric may be reduced, resulting ininformation loss. Under certain conditions, partial information can bepreserved and operation of the apparatus efficiency significantlyenhanced. This consequence will be addressed in greater detail herein.

There is a one-to-one correspondence between the information entropyH(x) emitted from the source per unit time and the values of the signalV_(src). The uncertainty of the source is given by;

${H\left( x_{V_{src}} \right)} = {- {\int{{p\left( x_{V_{src}} \right)}\log \mspace{11mu} p\frac{\left( x_{V_{src}} \right)}{m\left( x_{V_{src}} \right)}{\left( x_{V_{src}} \right)}}}}$

In this case

${p\left( x_{V_{src}} \right)} = {\frac{1}{\sqrt{2\; \pi {\langle P\rangle}}}^{- {(\frac{x_{V_{src}^{2}}}{2{\langle P\rangle}})}}}$

and

m(x_(x_(V_(STC))))

is a suitable normalization function for Shannon's differential entropy.where

P

is the average power of V_(src), proportional to the second moment ofthe signal of interest through efficiency. That is,

P

˜

V _(src) ²

˜

ηV _(src) ²

where

V_(src) ²

is the normalized power delivered to the apparatus.

Whenever the conditional uncertainties H_(y)(x)=H_(x)(y)=0 theninformation is conveyed and R is maximized, H(x)=H (y).

There is a correspondence between H(x) and the values of V_(src), anddynamic charges due to currents resulting from V_(src) and associatedcircuit impedances, through the association of symbols from an alphabetwith voltages as a function of time, V_(src)(t). The quantities ofinterest in phase space have an association with the degrees of freedomavailable through probability densities of V_(src)(t), (p_(v) _(src) ) adensity of states for the physical system is also implicit in therepresentation of uncertainty indicated by H(x)

∝−∫_(−∞) ^(∞) p _(v) _(src) ln [p _(v) _(src) ]d _(v) _(src) .

The physical degrees of freedom associated with S_(J) _(e) and S_(J)_(w) are dynamic quantities, defined by the disciplines of irreversiblenon-equilibrium based thermodynamics or extended irreversiblethermodynamics, using the concept of entropy flux whenever the system isnot in equilibrium. These flux variables are causally related tofunctions of H(x), H_(x)(y), H (y), H_(y)(x).

Expressions of physical entropies in flux may be recognized as morefamiliar concepts such as uncertainty in changes of phase and magnitudesof signals along with their corresponding time dependent fluctuatingcross-correlation functions. This includes the related signals ofinterest as well as spurious waveforms, harmonics, amplitude and phasenoise, and intermodulation distortions. Heat may be measured separately,though in some cases the list above demonstrates some thermaldependencies. The correspondence of these quantities and the functionaldescriptions that link them to various physical and information forms ofentropy is an embodiment of the present invention, which is anadvancement in the art. Likewise, the association of information usefulin communications application with the time dependent configuration ofmatter and energy at fundamental scales is also an embodiment of thepresent invention and is also an advancement in the state of the art.

RF modulation is the process of imparting information from theinformation source possessing H(x) to the complex envelope of the RFcarrier. In other words, the uncertainty metric quantified by H(x)possesses a physical counterpart mimicking the component symbolprobabilities in units of charge transfer per unit time. The resultingsignal takes the form

x(t)=a _(I)(t)cos(ω_(c) t)+a _(Q)(t)sin(ω_(c) t)

-   a_(I) (t) Δ Time variant In Phase component of the Carrier Envelope    also called the in-phase amplitude (component) or real amplitude    (component).-   a_(Q)(t) Δ Time variant Quadrature Phase component of the Carrier    Envelope also called the quadrature amplitude (component) or    imaginary amplitude(component).-   ω_(c) Δ Carrier Frequency≧0 radians/second

Any point in the complex signaling plane can be traversed by using theappropriate mapping of a_(I)(t) and a_(Q)(t). Alternatively, it ispossible to use a description based on the magnitude and phase of thecomplex carrier envelope. Battery operated mobile communicationsplatforms typically possess unipolar energy sources. In such cases, therandom variables defining a_(I)(t) and a_(Q)(t) are characterized bynon-central statistical parameters. A case of interest arises whenevera_(I)(t) and a_(Q)(t) are non-zero mean quasi-Gaussian. It is possibleto refer to this case as a complex non-zero mean Gaussian pdf orGaussian with 2 macroscopic statistical degrees of freedom, not to beconfused with the v of the apparatus. Analysis of the RF modulator andunipolar amplifier ought to consider the offset because of theassociated energy impacts. This can adversely affect the efficiency of atransmitter. A subsequent analysis provides a general treatment for anapparatus that transfers power to a load given a unipolar energy sourceand a signal that is approximately Gaussian. The signal plus offset maybe DC coupled or AC coupled to a load. In general, AC coupledcircumstances are more efficient. The analysis can be extended to thecomplex Gaussian case by deploying an apparatus for an in phase signaland one for a quadrature phase signal. The signal modulations defininga_(I)(t) and a_(Q), thus correspond to a 2-dimensional signaling spacethat can approach Shannon's capacity limit. This represents a classicalcase suitable for bounding performance of efficiency for signals thatpossess large PAPRs.

Circuits designed as embodiments of the present invention to accomplishthese modulations can fit many topologies and architectures. However,for linear modulations with unipolar offset, they reduce to two generalclasses for the amplitude envelope modulator, namely; series and shuntimpedance control. The following discussion progresses around thesemodels in terms of efficiency performance for series and shuntconfigurations as examples suitable for advancing concepts. Thetreatment for efficiency enhancement illustrated for the followingsimple models also enjoys common principles which apply to other classesof more advanced modulators. FIGS. 13 and 14 represent higher levelarchitectures which absorb modulator functions such as the ones to besubsequently discussed.

FIG. 8 shows a schematic 800 of a summing node with two input signalsand/or waveforms 878, 879 and one output signal 881. This summing node880 is a linear processing operator enabling the superposition of itsinputs. For example x(t) 878 may be a complex signal of interest andn(t) 879 may be a complex noise or interference process.

FIGS. 9A, 9B and 10A, 10B show examples of differential and single endedversions of the series modulator and shunt modulator topology,respectively. Two of these models may be used to create a complexsignal. These models represent examples for implementing some portion ofthe degrees of freedom for an apparatus which may be associated withmodulation derived from FLUTTER™ algorithm, for instance portions ofFIGS. 13 and 14. Examination of these models provide insight into thenature of efficiency enhancement.

In FIGS. 9A, and 9B, the impedance Z_(Δ) is variable from (0+0_(j))Ω to(∞+∞_(j))Ω. In these extreme states of the models, the power transfer isa maximum only when the series impedance is zero or when the shuntimpedance is infinite. Although these models may represent generalclasses of linear devices, depending on the selection of the compleximpedances, the models may be nonlinear as well. It is helpful to focuson those devices first that possess at least some non-zero realcomponents for Z_(s) Z_(L), and Z_(Δ). These models are hereafterreferred to as Type I models. They are useful for reference analysis anddo not represent specific implementation. For example, FIG. 9A shows adifferential Type I series modulator 900. This modulator 900 includesV_(s) 982, Z_(s)/2 983, 986, ZΔ/2 984, 987 blended control function{tilde over (ℑ)}{H(x)_(v,i)} 985, Z_(L) 988, and V_(L) 974 blendedcontrol function {tilde over (ℑ)}{H(x)_(v,i)} 985. FIG. 9B shows asingle ended Type I series modulator 910 embodiment that includes V_(s)982, Z_(s) 989 Z_(Δ) 990, V_(L) 974 and Z_(L) 988. Blended controlfunction {tilde over (ℑ)}{H(x)_(v,i)} 985 provides input to Z_(Δ) 990,changing its impedance in some proportion to a desired modulationamplitude with an appropriate statistic.

FIGS. 10A, 10B show a differential and single ended Type I shuntmodulator, respectively. The differential Type I shunt modulator 1000 ofFIG. 10A includes V_(s) 1082, Z_(s)/2 1083, Z_(Δ) 1090, Z_(L) 1088,V_(L) 1074, Z_(s)/2 1086. Blended control function {tilde over(ℑ)}{H(x)_(v,i)} 1085 provides input to Z_(Δ) 1090.

The single ended Type I shunt modulator 1010 of FIG. 108 includes V_(s)1082, Z_(s) 1089, V_(s) 1090, V_(L) 1074, Z_(L) 1088, blended controlfunction {tilde over (ℑ)}{H(x)_(v,i)} 1085. This shunt modulatorincludes a differential voltage source, V_(s) 1082, differential sourceimpedances Z_(s) 1089, differential shunt impedance Z_(Δ) 1090, and loadimpedance Z_(L) 1088. Blended control 1085 in both 1000 and 1010(configurations 1000,1010) provide a signal to Z_(Δ) 1090 in bothconfigurations, changing its impedance in some proportion to a desiredmodulation amplitude, with an appropriate statistic for output voltages.

As shown in FIGS. 9B and 10B, V_(s) (982, 1082, respectively) provides avoltage source. The control statistic for {tilde over (ℑ)}{H(x)_(v,i)}(985, 1085, respectively) can be fairly intricate depending on theimpedances Z_(s), Z_(Δ) and Z_(L) (i.e., 989, 1089, 990, 1090 and 988,1088, respectively). Z_(Δ)+Z_(s) must not equal zero in this (shunt)topology for practical application. The dynamics of {tilde over(ℑ)}{H(x)_(v,i)} (shown in FIGS. 9B and 10B as elements 985, 1085,respectively) are governed by a desired complex signal and the suitabletransforms (linear or nonlinear) to create the necessary statistic inV_(L) (shown in FIGS. 9B and 10B as element 974 and 1074, respectively).The voltage V_(L) 974, 1074, which changes as a function of Z_(Δ) 990,1090, controlled by {tilde over (ℑ)}{H(x)_(v,i)} 985, 1085 may thereforebe represented by the function of a complex phasor, where the subscriptsI, Q refer to in-phase and quadrature phase components of the signal,respectively.

V_(Δ) = {a(t)^(−ω t + θ(t))}${{a(t)}} = \sqrt{{a_{I}(t)}^{2} + {a_{Q}(t)}^{2}}$${\theta (t)} = {\left( {\arctan \mspace{11mu}\left\lbrack \frac{a_{Q}(t)}{a_{I}(t)} \right\rbrack} \right)({sign})}$a(t) ≡ Complex  Waveform  Amplitude

The sign operator keeps track of the complex signal quadrant and furtherdefines θ(t), which represents the phase angle. The phase angledescribes the angle of a vector representation of a complex signal.

FIGS. 13 and 14 illustrate two architectural methods of implementingmodulators based on FLUTTER™ and blended control-centric algorithmswhich can be used to render information bearing functions of time. Thesearchitectural methods can apply to the ongoing discussions concerningefficiency optimization. That is, the Type I modulator structures aswell as virtually any suitable modulator or encoding method may beabsorbed by FIGS. 13 and 14 for baseband or RF application.Architectural figures, such as, FIGS. 1, 2, 3, 4, 9A, 9B, 10A, 10B, 15,18, 20, 21, 22, 27, 28, 29, 30, 31, and 32 are relevant instantiationsrelated to aspects of discussions for FIGS. 13 and 14. Hence, thevarious functions, structures and modules illustrated in these, FIGS. 1,2, 3, 9A, 9B, 10A, 10B, 15, 18, 20, 21, 22, 27, 28, 29, 30, 31, and 32as well as their respective descriptions, are considered as possiblestructures and/or algorithms or modules which may be distributed as somesubset of the FIGS. 13 and 14 architectures and modules.

FIG. 13 illustrates an example of a general architecture 1300 suitablefor implementing the portion of the FLUTTER™ algorithm which encodes ormodulates information onto a waveform. The FLUTTER™ encoding ormodulation segment 1300 is capable of producing baseband signals as wellas RF signals at the output (1370). Load 1380 may be driven by output1370. A baseband signal may be produced by suitable choice of ω_(c) andφ in function/module 1341. Function/module 1341 can also become a localoscillator (LO) by suitable selection of ω_(c) the carrier frequency andthe phase of the carrier frequency. In the baseband mode ω_(c) and φ areselected along with amplitude (A) to render 1340 as a suitable constant.When the output signal 1370 is a carrier then ω_(c) selects theoperational frequency and φ sets the operational phase of 1340 the LOwaveform. Blended controls 1301 manipulate multiple degrees of freedomby adjusting the power source 1320 with output signals 1321 and MISOand/or compositing function 1360. The blended controls are functions ofsystem input entropy H(x), represented by {tilde over (ℑ)}{H(x)}_(v,i)where v, i are indices suitable for managing the controls. The blendedcontrols are generated in a vector synthesis engine (VSE) according tothe FLUTTER™ algorithm. k_(A) bits from the blended control areallocated 1302 to control the variable or switched energy or powersource 1320, to a desired resolution, maximizing efficiency for aminimum number k_(A)·k_(B) bits of control 1303 from the blended control1301 are allocated as additional degrees of freedom to generate aninformation bearing function of time via a MISO and/or compositingfunction 1360. k_(φ) bits of the control 1304 from the blended control1301 are allocated to select ω_(c) and/or φ to a desired value andresolution. In addition, both ω_(c) and/or φ may be functions of time.k_(A), k_(B), k_(φ) are allocated based on the number of availabledegrees of freedom for the apparatus, 1300, the efficiency for eachdegree of freedom, and the corresponding potential to distribute aspecific signal rate in each degree of freedom.

FIG. 14 illustrates an example of a general architecture 1400 suitablefor implementing a portion of the FLUTTER™ algorithm which encodes ormodulates complex information onto a waveform. The FLUTTER™ basedmodulator segment 1400 produces RF signals with corresponding output1470 that can accomplish universal modulation of a carrier. A localoscillator 1441 can be selected or adjusted for a carrier frequency,ω_(c), and phase φ, where one or both may be functions of time and aninput information source. The local oscillator (LO) waveform 1440 isdistributed in quadrature at a relative phase of 0° 1451 and 90° 1452with respect to waveform 1440 using a quadrature generating function1450. The MISO and/or compositing function module 1460 utilizes inputs1451 and 1452 as quadrature carrier inputs which may be frequency andphase agile functions of time (They may be modulated, and encoded withinformation). The output of module 1460 is an RF modulated signal 1470.The blended control 1401 are functions of system input informationentropy and generated by a vector synthesis engine (VSE). Controls 1402and 1404 select or adjust the variable or switched energy or powersources, 1420 and 1430 respectively, for in-phase and quadraturebranches of the MISO and/or compositing function 1460. The resolutions,in bits, for selecting power in these branches are k_(Q) _(A) and k_(I)_(A) , associated with waveforms 1421 and 1431. k_(Q) _(B) and k_(I)_(B) , are the number of bits from the blended controls 1403 and 1405respectively, providing additional degrees of freedom for thecompositing function 1460. k_(φ) is the number of bits of resolutionallocated for signal or waveform 1406 which selects or determines ω_(c)and φ in the LO function 1441 associated with signals or waveform 1440.k_(Q) _(A) , k_(Q) _(B) , k_(I) _(A) , k_(I) _(B) , and k_(φ) areallocated based on the number of degrees of freedom for the apparatus1400 the efficiency for each degree of freedom, and corresponding,potential to distribute a specific signal rate as well as information ineach degree of freedom. The output signal 1470 can be provided to load1480.

As efficiency increases, PAPR for the output signal typically decreases.It can be shown from fundamental principles that a lossless Type Imodulator possesses a thermodynamic efficiency of

$\eta \approx {\frac{1}{2\; {PAPR}}{\left( {{{i.e.\mspace{14mu} {when}}\mspace{14mu} Z_{s}} = 0} \right).}}$

A maximum efficiency results when the output signal PAPR=1 but this isnot consistent with amplitude modulation, of a_(I) and a_(Q). Thus toencode amplitude information PAPR>1 for the modulator. However, it ispossible to increase the total effective bandwidth as one possibleoption for expansion of phase space to maintain capacity while reducingPAPR, or provide multiple parallel channel branches for transport ofinformation. This can be represented topologically as shown in FIG. 15,which shows a parallel channel configuration to reduce PAPR per branch.

FIG. 15 shows a representation 1500 of a parallel “branched” channelconfiguration to reduce PAPR per branch according to an embodiment ofthe present invention. As shown in FIG. 15, H(X₁, X₂ . . . X_(v)) 1502is split, or fractured or distributed into component elements {tildeover (ℑ)}{H₁} 1504(a), {tilde over (ℑ)}{H₂}, 1504(b) and {tilde over(ℑ)}{H_(v)} 1504(n) (where “n” is any suitable number). These componentelements (generally 1504) have an associated metrics represented as

$\frac{C_{1}}{W_{1}}1505(a)\mspace{14mu} \ldots \mspace{14mu} \frac{C_{v}}{W_{v}}$

1505(n) (where “n” is any suitable number). The branches of 15 arejoined, or merged, or composited to obtain H(y₁, y₂ . . . y_(v)) 1575.This composite entropy function 1575, is associated with a rendering, orrepresentation of a desired information bearing function of time. It maybe an information bearing function of time, waveform, signal, RFmodulated carrier signal, or electronic data that can be converted,downloaded or reproduced as a rendered information bearing function oftime. It may also be some intermediate signal to be further processed.

A v branch channel may replace a single branch channel where each branchpossesses a lower PAPR. This is achieved by controlling the normalizedchannel capacity C_(v)/W_(v) (generally 1505) per branch such that;

C=C ₁ +C ₂ . . . C _(v)

Each ratio C_(v)/W_(v) (generally 1505) may be set as desired. Thederivations have assumed certain aspects of the waveform statistic inthe given bounds. Each separate branch of the composited channel canpossess a smaller PAPR and therefore a correspondingly greater η.However, the topological information flow indicated in FIG. 15, whichillustrates a distribution, or dispersal, of information in the form{tilde over (ℑ)}{H₁}, {tilde over (ℑ)}{H₂}, . . . {tilde over(ℑ)}{H_(v)}, (generally 1504) does not specify how the information isparsed to each path 1504(a) . . . (n) (where “n” is any suitable number)nor re-assimilated at an output node of composite entropy function 1575,from a physical model perspective. In general this can be accomplishedby weighting the use of each path to maximize efficiency whilstpreserving C to the greatest practical extent.

Whenever the output node of composite entropy function 1575 of theconceptual topology is constrained by a continuous time linearelectronic circuit model, it may be verified that summation of linearsignals in a physical sense also may use a v-way power combiner thatredistributes the energy of each separate branch 1504 whenever the vsignals are statistically independent.

FLUTTER™ permits the trade between efficiency and capacity bymanipulating smaller portions of phase space volume 1504(a) . . . (n)that collectively reconstitute 1575 statistically while regulatingdomain interactions. This can be a time-variant nonlinear operation. Thetime variant nonlinear operations may be distributed to each branch1504, absorbed by the

operator or some combination thereof. The domain interactions may bemanaged in a way that moderates the effects of multi-branch loadingphenomena described above through the proper design of

.

Consider the following volume of phase space which in general could behyper-geometric but is represented in FIG. 16 with a 3-dimensionalgeometry. FIG. 16 illustrates an example 1600 of a conceptual phasespace or pseudo-phase space, which has been arranged in three tierscorresponding to regions of differing energy levels, or energypartitions. Coordinates within the phase space are randomly highlightedto illustrate the arbitrary samples within partition ranges. The maxradii of the concentric scatter volumes roughly mark the energyboundaries. Each unique point in the space represents a member from asignal ensemble. FIG. 16 shows phase space 1600 with three axes. X-axis1602, Y-axis 1604 and Z-axis 1606.

It is not necessary to maintain symmetry of the volume and it may assumemany shapes depending on the corresponding apparatus constraints.However, it is instructive to maintain the total volume substantiallyconstant for purposes of this disclosure, though the shape could morph.By doing so, it is useful to conserve the total uncertainty foraccessibility to each coordinate within the space and therefore theinformation capacity of the space.

Let p({hacek over (η)}) be the probability density for the instantaneouswaveform efficiency associated with FIG. 9B. p({hacek over (η)}) can beused for both the series and the shunt cases and will be obtained tofacilitate an example.

Let p(V_(L)) be given approximately by;

${p\left( V_{L} \right)} = {\frac{1}{\sqrt{2\; \pi}\sigma_{V_{L}}}^{- \frac{{({V_{L} - {\langle V_{L}\rangle}})}^{2}}{2\; \sigma_{V_{L}}^{2}}}}$

The quantity (V_(L)−

V_(L)

) is also equal to {tilde over (V)}_(L), the AC signal. FIG. 11 depictsthis pdf (probability density function), which is a quasi-Gaussian pdf(probability density function) for Output Voltage, V_(L), with V_(s)=2,

V_(L)

=V_(s)/4(0.5V), and σ_(V) _(L) =0.15. FIG. 11 shows graph 1100 that hasX-axis (horizontal) 1102 showing V_(L) and Y-axis (vertical), 1104showing p(V_(L)). Curve 1106 is a plot of the Gaussian pdf (probabilitydensity function).

The average of the instantaneous efficiency, i), is obtained from;

$\overset{ˇ}{\eta} = {{\langle{{Re}\left\{ \frac{V_{L}^{2}}{\left( {V_{L}V_{s}} \right) - {Z_{r}\left( V_{L}^{2} \right)}} \right\}}\rangle} = {\langle\frac{P_{out}}{P_{in}}\rangle}}$

Also note the supplemental relationships;

Z_(L) = Z_(s)^(*) $Z_{r} = \frac{Z_{s}}{Z_{L}}$$V_{L_{\max}} = \frac{V_{s}}{2}$${\langle V_{L}\rangle} = \frac{V_{s}}{4}$$V_{L} = \frac{\overset{ˇ}{\eta}V_{s}}{\left( {1 + \overset{ˇ}{\eta}} \right)}$

The transformation,

${p_{\overset{ˇ}{\eta}} = {{p\left( V_{L} \right)}\frac{\left( V_{L} \right)}{\left( \eta_{i} \right)}}},$

enables the result;

${p\left( \overset{ˇ}{\eta} \right)} = {\frac{V_{s}}{\left( {1 + \overset{ˇ}{\eta}} \right)^{2}}\frac{1}{\sqrt{2\; {\pi\sigma}_{V_{L}}^{2}}}^{- \frac{{({\eta \frac{V_{s}\mspace{20mu} V_{s}}{{({1 + \overset{ˇ}{\eta}})}\mspace{14mu} 4}})}^{2}}{2\; {\pi\sigma}_{V_{L}}^{2}}}}$

{hacek over (η)} is an instantaneous waveform efficiency. It is not theproper thermodynamic efficiency. However, optimization of {hacek over(η)} can be shown to optimize proper thermodynamic efficiency undercertain conditions contemplated by the FLUTTER™ algorithm. Sometimesthis alternate efficiency metric ({hacek over (η)}) is a desirableobject of optimization.

A plot of this pdf (probability density function) is shown in FIG. 12 asgraph 1200. X-axis (horizontal) 1202 and Y-axis (vertical) 1204 are usedto plot a pdf (probability density function) 1206 for {hacek over (η)}given Gaussian pdf for Output Voltage. V_(L), with V_(s)=2,

V_(L)

=V_(s)/4(0.5V), and σ_(V) _(L) =0.15,

{hacek over (η)}

≅0.34.

The efficiency associated with FIG. 12 possesses an

{hacek over (η)}

of approximately 0.34. FIGS. 11 and 12 represent a starting referencepoint for enhanced efficiency example, given the assumption of thesimplified amplitude/envelope modulator models. The signal PAPR for thisexample is approximately 11.11.

One explanative example describes a method for using a portion of aFLUTTER™ algorithm to select energy partitions of the variable V_(L).The phase space from FIG. 16 corresponds to the partitions for therandom variable V_(L), as shown in FIG. 17, which shows an example plot1700. The X-axis 1702 shows V_(L) and the Y-axis shows p(V_(L)) 1704.Curve 1706 is shown as having three distinct portions. Portion 1716shows E₁, portion 1718 shows E₂ and portion 1720 shows E₃. An area undercurve 1706 is shown as 1714. Specifically, the plot 1700 of FIG. 17shows an approximate Gaussian pdf (probability density function) forOutput Voltage, V_(L), with V_(s)=2,

V_(L)

=V_(s)/4(0.5V), and σ_(V) _(L) =0.15 three Separate Energy Partitions,E₁, E₂, E₃. Note, the energies are actually the squared values for V_(L)over the indicated ranges.

In this example, the apparatus, as described herein, can be consideredas possessing three separate energy sources that are multiplexed at theinterface between the potential boundaries, V₁, V₂, (shown as elements1712 and 1713, respectively) as the amplitude statistic dictates.Voltages V₁ (1712) and V₂ (1713) may assume values from 0 to 1 volt asrequired for an application associated with the statistic of FIG. 17. Itis possible to define the domain association rule as;

E ₁ if; V _(L) <V ₁

E ₂ if; V ₁ ≦V _(L) ≦V ₂

E ₃ if; V ₁ <V ₂

Notice the distinction between the partitioned pdf (probability densityfunction) of FIG. 17 and the pdf (probability density function) of FIG.7. In FIG. 17 information is preserved across the energy domainboundaries while in FIG. 7 information is lost, or annihilated andenvironmental entropy is correspondingly increased. The situation ofFIG. 7 has been avoided for this example.

In the following discussion n can be a thermodynamic efficiency or aninstantaneous waveform efficiency depending on the suitable choice ofthe definition for (η) or pdf ({hacek over (η)}), a derived quantitybased on the signal statistic and circuit parameters and topology. Inthe case of a thermodynamic efficiency, the kernels of the integrals areconstant functions which are calculated from the ratios of pre averagedquantities,

⟨σ_(L)²⟩_(i)/⟨P_(in)⟩_(i) ⋅ ⟨σ_(L)²⟩_(i)

is the output signal variance (output signal power) of the i^(th)partition.

P_(in)

is the input power for the circuit in the i^(th) partition.

The calculations of

η

_(2, 3) may also be obtained from (where ζ is associated with athreshold index);

η

=k _(i) _(_) _(norm)∫_({tilde over (η)}) _(ζ−1) ^({tilde over (η)}) ^(ζ)ηp(η)d(η); i=1,2,3

i provides the domain (in this case the domain corresponds to partition)increment control for the calculations and k_(i) _(_) _(norm) provides anormalization of each domain such that each separate domain possesses acdf (cumulative distribution function) equal to a maximum measure of Iat the upper boundary. In some of the subsequent treatments k_(i) _(_)_(norm), or suitable equivalents, will be included in the factors λ_(i)also known as weighting factors. In some discussions these factors shallremain separate.

The following equations for averaged instantaneous efficiency andthermodynamic efficiency (respectively) apply to a Type I seriesdissipative modulator with a power source resistance equal to the loadresistance.

$\overset{ˇ}{\eta}\underset{\_}{\Delta}{\langle\frac{V_{L}^{2}}{{V_{L}V_{s}} - V_{L}^{2}}\rangle}$${\eta \underset{\_}{\Delta}\frac{\langle{\overset{\_}{\overset{\sim}{V}}}_{L}^{2}\rangle}{\langle{{V_{L}V_{s}} - V_{L}^{2}}\rangle}} = \frac{\sigma^{2}}{\langle P_{in}\rangle}$

Suppose we recursively apply this efficiency calculation to separatepartitions with the first boundary @ V₁=0.25 volts and the secondboundary @ V₂=0.75 volts. These thresholds correspond to a 2 bitresolution over a 1 volt dynamic range. In this circumstance theaveraged normalized efficiencies for the 3 regions are associated with aprobability weighting for each region;

Instantaneous Efficiency Weighting Factor

 {hacek over (η)}₁ 

 ≃ .674 λ₁ ≃ .035

 {hacek over (η)}₂ 

 ≃ .5174 λ₂ ≃ .928

 {hacek over (η)}₃ 

 ≃ .672 λ₃ ≃ .035

The final weighted average is;

{hacek over (η)}_(tot)

=η_(sx)(λ₁

{hacek over (η)}₁

+λ₂

{hacek over (η)}₂

+λ₃

{hacek over (η)}₃

)≃0.517

The final weighted average is;

{hacek over (η)}_(tot)

=η_(sx)(λ₁

{hacek over (η)}₁

+λ₂

{hacek over (η)}₂

+λ₃

{hacek over (η)}₃

)≃0.517

In this case, the switch efficiency η_(sx) is set to the value of 1.

The corresponding block diagram for an architecture associated with thiscalculation is shown as FIG. 18.

FIG. 18 shows a power switching module and series type 1 modulator 1800.This switching module and series modulator 1800 includes ℑ{H(x)_(v) ₁ ,H(x)_(v) ₂ , . . . H(x)_(v) _(i) } 1802, (a) . . . (n) (blended controlswhere “n” is any suitable number). If V_(s) ₁ 1812, V_(s) ₂ 1813 andV_(s) ₃ 1814. Blocks 1888, 1889 and 1890, which are impedancesassociated with a shunt modulator, are also shown. V_(L) 1874 isdeveloped by an output current flowing through Z_(L) 1888. As shown inFIG. 18, the apparatus 1800 transitions as each statistical boundary istraversed, selecting a new energy partition according to {tilde over(ℑ)}{H(x)_(v) ₁ , H(x)_(v) ₂ , . . . H(x)_(v) _(i) } (generally 1802).

The final weighted average of this solution for this particular FLUTTER™example has not yet been optimized. As will be discussed herein, aFLUTTER™ energy partitioning optimization algorithm can improve on theresults of this example.

From the prior example, it is possible to obtain an optimization of theform

max{

{hacek over (η)}_(tot)

}=max{λ₁

{hacek over (η)}₁

+λ₂

{hacek over (η)}₂

+λ₃

{hacek over (η)}₃

}

$\begin{matrix}{{\sum\lambda_{i}} = 1} \\{\min \left\{ {{H(x)} - {H(y)}} \right\}}\end{matrix}$

It is also noted that

{hacek over (η)}₁

={tilde over (ℑ)}{V _(s) ₁ },

{hacek over (η)}₂

={tilde over (ℑ)}{V _(s) ₁ ,V _(s) ₂ },

{hacek over (η)}₃

={tilde over (ℑ)}{V _(s) ₂ ,V _(s) ₃ }

The overall goal is to solve for the optimum energy partitions E₁, E₂,E₃ (see FIG. 17, elements 1716, 1718 and 1720, respectively) byselecting the most efficient voltages V_(s) ₁ =2V₁, V_(s) ₂ =2V₂, V_(s)₃ =2V₃·V_(s) ₃ is selected as the maximum available supply by definitionand was set to 2V for the prior example. The minimum available voltageis set to V_(s) ₀ =0. Therefore only V_(s) ₁ and V_(s) ₂ are calculatedfor the optimization that simultaneously (or concurrently or inparallel) determines λ₁, λ₂ and λ₃ for this particular scenario.

For the present, assume that H(x)−H (y) can be minimized so that thedesired signal is faithfully composited. This is accomplished bymanipulating i degrees of freedom as well as other degrees of freedom inthe modulator, for example the V_(t) degrees of freedom associated withZ_(Δ) 1890, of FIG. 18. Then application of the maximization algorithmmax{

{hacek over (η)}_(tot)} may be solved using the calculus of variationsto obtain solution for V_(s) ₁ and V_(s) ₂ .

The improved solution for this 3 partition example becomesV_(s1)=2V₁≃0.97, V_(s2)=2V₂≃1.3V. The comparative domain efficienciesand weightings are given by;

Instantaneous Efficiency Weighting Factor

 {hacek over (η)}₁ 

 ≃ .667 λ₁ ≃ .466

 {hacek over (η)}₂ 

 ≃ .396 λ₂ ≃ .399

 {hacek over (η)}₃ 

 ≃ .566 λ₃ ≃ .141and the final total average is

{hacek over (η)}_(tot)

≈0.692.

Thus, the FLUTTER™ energy partition optimization solution provides anoticeable improvement over an arbitrary 2 bit assignment forthresholds. Moreover, the improvement over a single power sourcepartition is approximately a factor of 2 or 100% improvement of theinstantaneous waveform efficiency metric.

The FLUTTER™ algorithm demonstrates that application of optimalthresholds is not ad hoc or arbitrary. For instance, ad hoc binaryweighting was illustrated to be inferior to a FLUTTER™ optimization.Standard Legacy envelope tracking schemes which have been digitized donot optimize according to a FLUTTER™ algorithm and therefore aredifferent as well as inferior. A significant benefit of FLUTTER™ isevident in the relatively reduced number of partitions required toprovide relative efficiency enhancement. In addition, the partitionselection rate may be reduced when additional information entropy isdistributed in alternate degrees of freedom. Furthermore, the otherdegrees of freedom v restore information in the signal envelope notaccommodated by the sparse number of partitions. These v degrees offreedom also smooth and/or interpolate the envelope to a desiredstandard. Legacy approaches and technologies do not restore an envelopeusing a small number of quantization levels for power supply enveloperestoration or envelope following.

When it is desired to ascertain an optimal theoretical solution for bothnumber of energy partitions and their potentials for the case whereamplitude is exclusively considered as a function of any statisticaldistribution p(V_(L)) (shown in FIG. 11 as Y-axis 1104, FIG. 13 asY-axis 1304 and FIG. 17, Y-axis 1704 as an example). It is reasonable tobegin by using PAPR and

η

definitions.

${PAPR}\mspace{11mu} \underset{\_}{\Delta}\frac{P_{out\_ peak}}{\langle P_{out}\rangle}$${{{\langle\eta\rangle}\underset{\_}{\Delta}\frac{\langle P_{out}\rangle}{\langle P_{in}\rangle}}\therefore{\langle\eta\rangle}} = \frac{P_{out\_ peak}}{({PAPR})\mspace{11mu} {\langle P_{in}\rangle}}$

This defines

η

for a single energy partition. The following expression may be used fori energy partitions:

${\langle\eta\rangle} = {{\sum\limits_{i}{\langle{\eta_{i}\lambda_{i}}\rangle}} = {{\sum\limits_{i}\frac{P_{{out}_{i}}\lambda_{i}}{({PAPR})_{i}\mspace{11mu} {\langle P_{{in}_{i}}\rangle}}} = {\sum\limits_{i}{\lambda_{i}\frac{\langle P_{{out}_{i}}\rangle}{\langle P_{{in}_{i}}\rangle}}}}}$

From the 1^(st) and 2^(nd) Laws of Thermodynamics, it can be determinedthat

$\frac{\langle P_{{out}_{i}}\rangle}{\langle P_{{in}_{i}}\rangle} \leq 1$⟨η_(i)⟩ ≤ 1

λ_(i) is the statistical weighting for η_(i) over the i^(th) partitionso that

${\sum\limits_{i}\lambda_{i}} = 1$

Given these conditions, it is possible to write the followingoptimization

${{\langle\eta\rangle}\underset{\_}{\Delta}\max \left\{ {\sum\limits_{i}\; {\eta_{i}\lambda_{i}}} \right\}} = {\max \left\{ {\sum\limits_{i}{\lambda_{i}\frac{\langle P_{{out}_{i}}\rangle}{\langle P_{{in}_{i}}\rangle}}} \right\}}$

Thus, each and every η_(i)→1 for

η

to become one. That is, it is impossible to achieve an overallefficiency of

η

→1 unless each and every partition is also 100% efficient. Hence,

${\max \mspace{14mu} {\langle\eta\rangle}} = {{\sum\limits_{i}\lambda_{i}} = 1}$

It has already been shown that the λ_(i) are calculated as the weightsfor each i^(th) partition such that;

λ_(i) = ∫_(V_(L(ζ − 1)))^(V_(L_(ζ)))p(V_(L)) V_(L)

It follows for the continuous analytical density function p(V_(L)) that

λ_(tot) = ∫₀^(V_(L_(max)))p(V_(L)) V_(L) = 1${Analogously},{{\sum\limits_{i}\lambda_{i}} = {{\int_{0}^{V_{L_{\max}}}{{p\left( V_{L} \right)}\ {V_{L}}}} = 1}}$

As stated herein, it is possible to generalize the prior optimizationprocedure to emphasize the calculation of sufficient partitions whichcan approach an acceptable tradeoff efficiency,

η

, yet minimizes the number of energy partitions according to practicalresource constraints.

Turning now to a discussion of the efficiency gains vs. the number (i)when (i) is finite: Efficiency gain, vs. complexity, technologyrestrictions and perhaps cost would set an upper lower bound on (i).

The generalized η optimization procedure (Type I modulator) may beprescribed for setting partition threshold a_(ζ). ζ will be used anindex associated with threshold number at the boundary of the partition.The number of thresholds is one less than the number of partitions. Thedifferences between adjacent threshold are considered as differentialquantities in this example.

${\max \left\{ \eta_{tot} \right\}} = {\max \left\{ {\sum\limits_{i}{\lambda_{i}k_{i_{norm}}{\int_{\alpha_{\{{\zeta - {1.\zeta}}\}}}^{\alpha_{\zeta}}{{\overset{\sim}{\alpha}}_{\zeta}{p\left( {\overset{\sim}{\alpha}}_{\zeta} \right)}\ {{\overset{\sim}{\alpha}}_{\zeta}}}}}} \right\}}$

${\alpha_{\zeta}\underset{\_}{\Delta}\frac{V_{L_{\zeta}}^{2}}{{V_{L_{\zeta}}V_{S_{\zeta}}} - {Z_{r}V_{L_{\zeta}}^{2}}}},{\alpha_{\lbrack{{\zeta - 1},\zeta}\rbrack}\underset{\_}{\Delta}\frac{V_{L_{\zeta - 1}}^{2}}{{V_{L_{\zeta - 1}}V_{S_{\zeta}}} - {Z_{r}V_{L_{\zeta - 1}}^{2}}}}$${\overset{\sim}{\alpha}}_{\zeta}\underset{\_}{\Delta}\frac{V_{L}^{2}}{{V_{L}V_{S_{\zeta}}} - {Z_{r}V_{L}^{2}}}$${{{\overset{\sim}{\alpha}}_{\zeta}} = {\left( \frac{V_{s}}{\left( {V_{s} - {Z_{r}V_{L}}} \right)^{2}} \right){V_{L}}}},{\zeta = 1},2,{{3\mspace{14mu} \ldots \lambda_{i}} = {\int_{V_{L_{\zeta - 1}}}^{V_{L_{\zeta}}}{{p\left( V_{L} \right)}\ {V_{L}}}}}$$\sum\limits_{i}\; {\lambda_{i}\underset{\_}{\Delta}1}$$V_{L_{\zeta}}\underset{\_}{\Delta}\frac{V_{S_{\zeta}}}{2}$$Z_{r}\underset{\_}{\Delta}\frac{Z_{s}}{Z_{L}}$Z_(s) ≡ Modulator  Energy  Source  ImpedanceZ_(L) ≡ Modulator  Load  Impedance

FIG. 19 shows a graph 1900 that illustrates the trend of {hacek over(η)} plotted on Y-axis (vertical) 1904 as a function of the number ofpartitions, plotted on X-axis (horizontal) 1902, as curve 1906.Specifically, FIG. 19 shows instantaneous waveform efficiency (plottedas curve 1906) as a function of energy partition number for an exampleof a Type I modulator model processing signal amplitudes characterizedby non central Gaussian statistics, for a particular Z_(r). Notice howthe {hacek over (η)} (instantaneous efficiency) is greatly enhanced forthe allocation of only several partitions.

It can be shown that the thermodynamic efficiency η and theinstantaneous efficiency {hacek over (η)}, for this modulator, arerelated by (for a single energy partition);

$\eta \approx \frac{1}{{\frac{V_{s}}{\langle V_{L}\rangle}{PAPR}_{sig}} + {\left( {\frac{1}{\overset{ˇ}{\eta}} - \frac{V_{s}}{\langle V_{L}\rangle}} \right)\left( {PAPR}_{sig} \right)}}$

PAPR_(sig) is the peak to average power ratio for the signal portion ofthe waveform.

Thus, increasing {hacek over (η)} also increases η where 0≦{hacek over(η)}≦½ for a Type I modulator.

Although the particular optimization is in terms of {hacek over (η)}suitable efficiency choices such as η={tilde over (ℑ)}{{hacek over (η)}}may also be directly optimized. In particular, the thermodynamicefficiency

$\eta = \frac{\langle P_{out}\rangle}{\langle P_{in}\rangle}$

may also be directly optimized. An additional example will illustratethe results of optimizing thermodynamic efficiency using a directapproach.

Suppose that the prior example is modified so that a nearly Gaussiansignal of ˜11.1 PAPR is produced at the output load of a type 1modulator. Furthermore, suppose that the source resistance is negligibleand may be approximated as zero. Now the signal of interest at theoutput can vary between zero volts and v_(s)=2V. We may apply the sameprocedures as before to obtain results for the proper thermodynamicefficiency. Furthermore, we calculate the efficiency improvementobtained for the partitioning algorithm compared to a modulator with asingle power source. The result is indicated in a graphic plot 3901 inFIG. 39 thermodynamic efficiency improvement η_(i)/η₁ vs. partitionnumber. Notice that the percentage improvement is 40% for 2 partitions,54% for 3 partitions and 73.5% for 8 partitions. The ratio is theefficiency for the modulator using i partitions divided by theefficiency for a single power source based modulator. Thus, whenFlutter™ is applied and optimal thresholds for partitions employed, onlya few power source partitions are required for significant thermodynamicefficiency improvement.

This optimization procedure is in general applicable for all forms ofp(V_(L)) (and therefore different modulator types) even those withdiscrete Random Variables (RVs), provided care is exercised in definingthe partition boundaries and domains for the RV. In this manner verycomplex Probability Distribution Functions (PDFs) with pdf (probabilitydensity functions) subspaces may be processed, though calculation ofsolutions can prove challenging.

Nevertheless, there are several solution techniques that yield favorableresults. Locations of the potentials V_(L) _(ζ) are not uniformly spacedalong the V_(L) axis. Likewise, λ_(i) are not equally weighted ingeneral. However, as ζ or consequently i becomes quite large thepartitions obtain greater parity. It is an embodiment of the presentinvention that moderate to low values for ζ or i, demand optimizedpartition differentials with threshold boundaries that are notnecessarily coincident with quantization differentials or samplethresholds used in envelope restoration or envelope trackingreconstructions. In addition to the prior comments, it should be notedthat a change in source impedance of power sources may change efficiencyand the threshold optimization of partitions.

In terms of the information quality that has been introduced;

min{H(x)−H(y)}

This calculation may also be approximated by a more tangible associatedmetric that is particularly convenient for lab application as mostmodern signal analyzers may be equipped with cross-correlation or otherrelevant error metric measurement capabilities. The minimization isoften accomplished by one of several means;

-   -   Calculation of Error Vector Magnitude (EVM)    -   Calculation of Minimum Mean Square Error (MMSE)    -   Calculation of Cross-Correlation and/or Covariance

Cross-correlation is addressed since it maintains continuity of thepresent themes. It is possible to define the cross-correlation betweeninput and output as (x→input variable, y→output variable)

R _(xy)=∫_(−∞) ^(∞)∫_(−∞) ^(∞) xyp(y,x)dxdy

This form is a statistical cross-correlation. The cross-covariance whichmay be used in certain circumstances is the same operation afterextracting the mean values of x, y. It is noted that the y variable isoften normalized or scaled to compensate for test system scaling.

Now the example as presented would appear perfectly linear in conceptsince V_(L) 1874 should be a faithful reproduction of {tilde over(ℑ)}{H(x)_(v,i)} 1802 by definition. However, in a practical system witha more complicated modulation requirement, Z_(Δ) 1890, may bedistributed with many controls. Voltages 1812, 1813, 1814, may benonlinear and each may be determined by multiple controls. In suchcases, imprecision, quantization noise and a host of other variables maypotentially compromise the desired cross-correlations thereby increasingS_(J) _(w) . Hence, the cross-correlation or cross-covariance orcovariance metric or a reasonable similar metric may be employed toassess the particular synthesized architecture. Statistical calculationsfor the cross-correlation may be used whenever p(x,y) can be obtained orsuitably approximated. In cases where this is not convenient, the timecross-correlation may be employed for a conditionally-stationary randomprocess. This form of cross-correlation is given by;

${R_{xy}(\tau)} = {\lim\limits_{T_{O_{cc}}\rightarrow\infty}{\int_{- T_{O_{cc}}}^{T_{O_{cc}}}{{x(t)}{y\left( {t + \tau} \right)}\ {t}}}}$

-   T_(O) _(cc) Δ Observation Time Interval for Cross-Correlation

The input and output spectral masks are compared from;

∫_(−∞) ^(∞) R _(x)(τ)e ^(−jωτ) dτ−∫ _(−∞) ^(∞) R _(y)(τ)e ^(−jωτ) =S_(c)(ω)

where R_(x)(τ) and R_(y) (τ) are suitable auto correlations.

In this manner compliance can also be assessed in the frequency domain.Other comparison metrics are useful as well, such as covariance, MMSE,phase error versus frequency, phase error versus time, and variationsthereof.

E. T. Whittaker published a paper in 1915 concerning the interpolationof functions. Shannon borrowed this theory and that of Nyquist to obtainthe cardinal series for sampling, given by

${X(t)} = {\frac{1}{\pi}{\sum\limits_{n = {- \infty}}^{\infty}\; {{X\left( \frac{n}{2\; W} \right)}\frac{\sin \left\lbrack {\pi \left( {{2W\; t} - n} \right)} \right\rbrack}{{2\; W\; t} - n}}}}$W ≡ Bandwidth η ≡ Sample  Number t ≡ Time

A finite information bearing function of time may be reproduced bysuitable application of the Cardinal series. Shannon went on to showthat the number of samples sufficient for reconstruction of any waveformof finite duration τ using the Cardinal series is given by Shannon'snumber N_(s).

N _(s)=2Wτ

In the most general case for n→large and samples obtained from X(t),which may be composed of an arbitrary sum of Gaussian random variables,there exists a hyperspace containing the hyper sphere with volume givenby;

$V_{n} = {\frac{\pi^{n/2}}{\Gamma \left( {\frac{\pi}{2} + 1} \right)}\left( {2\tau \; {W\left( {{\langle P\rangle} + N} \right)}} \right)^{n}}$⟨P⟩ ≡ Average  Signal  Power⟨N⟩ ≡ Average  Gaussian  Noise  Power

This hyper sphere possesses an analog in statistical mechanics relatedto the states of particles in phase space, where the coordinates inclassical phase space are defined by momentum p and position q,respectively. The probability densities for the degrees of freedom andtheir energy distributions, as well as corresponding informationdistributions, have been absorbed into the construct of applicationphase space at a higher level of abstraction for the purpose of thisdisclosure. This higher level of abstraction may also be referred to asa pseudo-phase space.

As noted, i→∞ whenever the pdf (probability density function) is parsedin infinitesimal differential increments. In practice, modern daycommunications systems often quantize the variable (V_(L)) associatedwith an output voltage across a load impedance. Even though it may becontinuous or discrete at the source, it is often quantized at theapparatus interface. N_(s)=2Wτ is a prescription for the number ofsamples over the dimensionality of signal space to reconstruct themessage without losing information. The Nyquist sample rate then isgiven by;

$R_{N} = {\frac{N_{s}}{\tau} = {2W}}$

N_(s) samples amongst the i partitions will distribute according to theprobability density p(V_(L)) and the ancillary rules that assign therespective domains. These samples are only partially utilized by theenergy partitioning facilities of the apparatus. Additional samples maybe required to support v degrees of freedom. In general, it is possibleto assign i≦2^(k) partitions to enable an efficient system. The averagefrequency of samples within each bin (a bin may be thought of as asubset of values or span of values within some range or domain) can becalculated from;

$\mspace{20mu} {\Delta \; V_{L}\underset{\_}{\Delta}\frac{V_{L_{{ma}\; x}}}{2^{k}}}$$\mspace{20mu} {{p_{\Delta \; V_{L_{i}}}{\underset{\_}{\Delta}\left( {\int_{V_{L_{i - 1}}}^{V_{L_{i}}}{{p\left( V_{L} \right)}{V_{L}}}} \right)}} = \lambda_{l}}$Δ V_(L) ≡ Average  Voltage  Increment  per  Sample

The number of samples per bin is thus N_(s)·pΔv_(l) _(i) . Additionally,2^(k) sets the sampling resolution for the system.

The potential between fixed and/or sampled energy partitions can begreater than or equal to V_(L) _(max) /2^(k) specifically set by theFLUTTER™ algorithm to realize an optimized efficiency gain. The rulesfor assigning the number and frequency of the samples N_(s) to each ofthe i bins may be directly attributed to the mapping of H(x) symbolemission to V_(L) and (V_(L)), via {tilde over (ℑ)}{H(x)_(v,i)}.

Note that optimal assignment of partition boundaries is very specific(according to FLUTTER™) and will not in general correspond to binarysampling thresholds determined solely from interpolation theory orenvelope tracking/restoration theories.

(i) energy partitions with properly assigned sample clusters, n_(i),preserve the sampling space and therefore the information space. Thesample clusters fall within the boundaries of the i^(th) energypartition and are further processed by other degrees of freedom toenhance efficiency and quality metrics of the signal. These additionaldistinct degrees of freedom have also been enumerated by an index v. Thev degrees of freedom within the modulation method described herein canspan a portion of, a single, or all i partitions.

The number of partition transitions per unit time per degree of freedomfluctuate in each path of a FLUTTER™ algorithm according to signalstatistics and therefore these partition sampling events may be slowerthan the final composited signal envelope Nyquist sampling rate orbandwidth. The additional (non-energy partition selection) requiredsignal reconstruction sample clusters are distributed to other degreesof freedom and composited through other blended control paths, thuspreserving the requirements of the sampling theorem. This is a preferredapproach given the minimum fixed number of energy partitions topractically achieve a specified efficiency.

Reconstruction of a sampled signal envelope by linear interpolationand/or filtering such as the type used in Legacy envelope tracking andenvelope restoration techniques, does not constitute an efficiencyoptimization algorithm. An efficient algorithm should also accommodatesimultaneous or joint (or concurrent or parallel) optimization max{η},min{H_(x)−H_(y)}. If joint dependency of efficiency and quality are notexplicitly contemplated then the algorithm is ‘ad hoc’.

As described above, it is useful to substantiate that the variable foramplitude of a signal may be quantized and that the energy partitions beless than or equal to the number of quantization levels. This is aflexible, or loose, upper bound. The idea of quantization is justifiedsince the continuous random variable V_(L) can be exactly reproducedaccording to the sampling theorem and could correspond to an efficiencyoptimization without requiring an infinite number of differentiallyspaced partition potentials.

FIGS. 20 and 21 show examples of a Type II modulator model for seriesand shunt realization, respectively. Equivalent differential topologiesare possible and may be assumed in the treatment just as single endedand differential topologies were included for Type I models, asdescribed herein.

FIG. 20 shows an example of a series Type II modulator 2000. Thismodulator 2000 includes a phase/frequency control input 2092, timevariant source voltage K. 2082, source impedance Z_(s) 2089. Also shownis variable branch impedance Z_(L), 2090, which receives control inputfrom amplitude control 2091 and signal input from source V_(s) 2082. Theoutput from Z_(Δ) 2090 is provided to Z_(L) 2088 and V_(L) 2074. V_(s)2082, may for example be an agile RF carrier with phase modulation fromcontrol 2092. The amplitude of V_(L) 2074 may be changed by changingZ_(Δ) 2090 via control 2091. Therefore, output V_(L) may be phasemodulated and amplitude modulated through changes imparted by controls2092 and 2091.

FIG. 21 shows an example of a shunt Type II modulator 2100. Thismodulator 2100 includes a phase/frequency control input 2192, timevariant source voltage V_(s) 2182, Z_(s) 2189. Also shown is a variableimpedance Z_(Δ) 2190, which receives control input from amplitudecontrol 2191. The impedance from Z_(Δ) 2190 is in parallel with Z_(L)2188 and affects the amplitude of V_(L) 2174. The output voltageamplitude of V_(L) 2174 and phase of V_(L) 2174 may be changed byvarying controls 2191 and 2192.

The series modulator instantaneous waveform efficiency can be derivedsimilar to the methods developed for analyzing the Type I modulators.The partially reduced result is;

$\overset{˘}{\eta} = {{\langle\frac{P_{{out}_{WF}}}{P_{i\; n}}\rangle} = {\langle{{Re}\frac{V_{L}^{2}}{{V_{s}V_{L}} - {V_{L}^{2}\left( {Z_{s}/Z_{L}} \right)}}}\rangle}}$

It is noted that the efficiency 7) reduces to that of the Type I modelwhen the overhead for creating a sine wave from a fixed potential isminimal. However, if D.C. blocking is used, for example a capacitor orhigh pass filter in series with the load output of Z_(s) 2089,efficiency may be increased.

In addition it is verified that Type II shunt model yields approximatelythe following provided the condition of a short circuit is avoided.

$\overset{˘}{\eta} = {{\langle\frac{P_{out}}{P_{i\; n}}\rangle} = {\langle{{Re}\left\{ \frac{\langle V_{L}^{2}\rangle}{{V_{s}V_{L}} - {V_{L}^{2}\left( {Z_{s}/Z_{L}} \right)}} \right\}}\rangle}}$

The proper thermodynamic efficiency

P_(out) _(sig)

/

P_(in)

=η also increases as {hacek over (η)} increases for these Type IImodulator examples. Again, the use of a D.C. blocking circuit such ascapacitor or other filter, as part of Z_(s) 2189 may improve efficiencyin this case.

Hence, the Type II modulator models follow the Type I model performanceclosely over significant dynamic range of the relevant signals. Onepossible difference is the explicit inclusion of an oscillator sourcewith phase/frequency control as a unique control. A plurality of Type Imodels can also create complex passband signals. Also Z_(Δ) 2090, 2190,may be in general a complex function and its control may likewise beconsidered as a complex number, thus suitable for complex envelopegeneration. However, a Type II model is convenient for complex signalgeneration since the controls may be independently manipulated by scalarfunctions if desired. However, reserving the ability to drive Z_(Δ)2090, 2190 by a signal consisting of complex numbers can offer somedesirable degrees of freedom. The complex numbers may control the realand imaginary portions of the complex impedance Z_(Δ) 2090, 2190. Manyuseful complex signaling scheme can be realized with this model byapplying the circuit architectures of FIGS. 20 and 21 to in-phase andquadrature-phase modulation schemes.

As described herein, the focus has been on discussions of optimizationof thermodynamic efficiency, η, with respect to application variableenergy partitions applied to modulation techniques, such as thosetechniques using any modulator technology, or such as d2p™ technology.It is useful to develop the similar efficiency themes but relate thediscussion to the encoding of the information metric H(x) into phase,since this is a significant macroscopic degree of freedom for signalsand such agility is helpful for modern signaling standards.

There is a common assumption in the communications industry thatconstant envelope signals given by;

|a(t)|=√{square root over (a _(I)(t)² +a _(Q)(t)²)}=constant

possess maximum efficiency performance. This rule of thumb isapproximately true under restricted circumstances but becomes challengedas capacity increases for at least two reasons. The application phasespace is smaller dimensionally whenever amplitude modulation is deniedand therefore capacity decreases for specified link performance. Thisusually demands greater transmitter power and bandwidth to offsetcapacity losses. In fact, regulatory and standards body restrictionsrender some phase modulation waveforms as obsolete or of narrowapplication, so as to have limited use.

In addition, the phase modulation, when required to support greaterinformation rates, begins to impact the efficiency of practicalinfrastructure electronics. This is especially true for significanttransmitter power requirements. Changing phase of a carrier atincreasingly greater rates corresponds to accelerating and deceleratingelectrons, which have mass and are also associated with thecorresponding electromagnetic fields of radiation possessing momentum.The greater the increase or decrease (+/−) accelerations of theelectrons and the uncertainty of their changes, the greater the impacton the efficiency of practical phase modulation schemes. The changinginertia associated with accelerating and decelerating electrons andtheir fields requires more energy than the case where currents arerelatively constant.

Nevertheless, it is also true in practice that phase modulation can be apowerful technique to conserve energy if the phase changes are properlycontrolled and of moderate rates. The most beneficial solutions addressboth amplitude and phase, which is assumed in the subsequent portions ofthis disclosure.

Embodiments of the present invention are also directed to criteria forobtaining energy partitions, which can enhance efficiency for RFmodulation processes which includes amplitude and phase modulatedsignals. The signal envelope magnitude often drives these criteria andthe greater the uncertainty metric H(x) the greater the uncertainty forthe signal envelope. Rapid and uncertain carrier phase fluctuations, canalso impact efficiency. Unipolar signals can be defined as beingpositive so that 0≦a(t)≦V_(L) _(max) . This range is parsed into (i)domains consistent with the FLUTTER™ algorithm to improve efficiency. vdegrees of freedom may also be independently deployed to controlsignaling degrees of freedom within the modulation, such as d2p™modulation, so that signals may be reconstructed, or rendered,accurately while optimizing efficiency. v degrees of freedom may alsocontrol magnitude and phase of the complex signal given the constraintsimposed within the i^(th) energy partition. The indices, v, i thus pointto portions of information space {tilde over (ℑ)}{H(x)_(v,i)} which areaccessed to generate the physical expression of the v domains. A finaloutput is obtained as a function of blended controls according to

a(t)e ^(jω) ^(c) ^(t+θ(t)) ={tilde over (ℑ)}{H(x)_(v,i)}

E_(e) _(out) the effective energy in the output signal and the wasteenergy E_(w) _(out) , are given by;

$E_{e_{out}} = {\sum\limits_{v}^{\;}{\sum\limits_{i}^{\;}{{\lambda_{v_{i}}\left( \eta_{v_{i}} \right)}E_{s_{v_{i}}}}}}$$E_{w_{out}} = {\sum\limits_{v}^{\;}{\sum\limits_{i}^{\;}{{\lambda_{v_{i}}\left( {1 - \eta_{v_{i}}} \right)}E_{s_{v_{i}}}}}}$E_(s_(v_(i))) = E_(e_(out)) + E_(w_(out))

E_(e) is maximized and E, is minimized. In order to accomplish thisoptimization, the effective entropy flux,

S_(J_(e_(i))),

is generated so that waste entropy flux

S_(J_(w_(i)))

is minimized. The term “effective entropy flux” and “waste entropy flux”as applied here refers to perturbations of phase space that impartinformation through physical means. Such fluctuations possess relativelyshort time constraints on the order of a symbol duration compared tothermal equilibrium, which can take many symbols to stabilize. Hence,the fluctuations they may be analyzed using methods of extendednon-equilibrium thermodynamics.

E_(e) is the effective output signal energy. One quality of the E_(e)metric is given by;

${\langle\eta\rangle} = \frac{\langle E_{e}\rangle}{\langle{E_{e} + E_{w}}\rangle}$

The other quality metric can be related to the difference inuncertainties H(x) and H(y) for the input and output of the modulationprocess respectively;

min{H _(x) −H _(y)}≦ε

ε can be an arbitrarily small number which may be estimated using errorvector magnitudes and minimum mean square error techniques whichcalculate energy differences between the input variable x and outputvariable y. As a consequence, the additional metric

max {S_(J_(e_(i))) − S_(J_(w_(i)))}

becomes important because the entropy flux captures the system stateuncertainty in a context which ties the emission of symbols from H_(x)to phase space perturbations expressed by

S_(J_(e_(i))).

Each symbol emitted from the information source is distributed intomultiple FLUTTER™ algorithm branches, which may be in general nonlinear.Therefore, as previously described, the nonlinear tradeoff forefficiency should be balanced with the concern for information loss.This tradeoff is managed by the FLUTTER™ algorithm and BLENDED CONTROLFUNCTION BY PARKERVISION™.

FIG. 22 is another illustration of a blended control functiondistribution architecture which processes vectors of FLUTTER™ algorithmvalues per each sample or state. These parallel vector states enable vdegrees of freedom and i partitions to synthesize portions ofsubordinate signals with statistical co-dependencies. A vector synthesisengine (VSE) module 2203 calculates the blended control function andrenders the parallel control vector per sample of the informationbearing function of time. In this example architecture each of the v_(i)processing branches possesses its distinct set of degrees of freedom andi^(th) energy partition. The degrees of freedom and partitions mayoverlap domains between the branches. The prominence of each branch orthe weighting of each branch is a random variable λ₁ (part of 2211 a)through λ_(i) (part of 2211 n) (effective weighting factors) and eachbranch will possess a corresponding variable efficiency through {tildeover (η)}_(i). The variable efficiency {tilde over (η)}_(i) may also beexpressed in terms of {hacek over (η)} and/or η the instantaneous andthermodynamic efficiencies respectively.

The subordinate signals are in general complex quantities, which arefunctions of the final desired output amplitude a_(n) and phase Θ_(n) atn^(th) the sample. Each branch may possess a nonlinear characteristicand a final signal synthesis is composited through the action of theoutput operator

2217 and distributed blended controls that optimally integrates eachstatistically weighted nonlinear branch.

FIG. 22 is a diagram that illustrates one embodiment 2200 and howinformation and energy partitions may be organized in terms oftopological signal flow. This representation 2200 shows assignment ofinformation resources to each branch with consideration of nonlinearity.As shown in FIG. 22, flow diagram 2200 includes portions of VSE (VectorSynthesis Engine) 2203. The VSE module 2203 generates ℑ{H_(v,i)} 2205(a). . . (n) (where “n” is any suitable number). These functions (generally2205) v₁ . . . v_(i) and produce an associated energy, E_(s) ₁ 2207 (a),E_(s) ₂ 2207 (b) and E_(s) _(i) 2207 (n) (where “n” is any suitablenumber) and a derived function 2209(a) . . . (n) (where “n” is anysuitable number). The output of function 2209(a) . . . (n) (generally2209) is shown as 2211 (a) . . . (n), respectively (generally 2211). Thesignals 2211(a) . . . (n) are provided to and associated with NL₁ 2215(a), NL₂ 2215 (b) . . . NL_(i) 2215 (n) (where “n” is any suitablenumber). The outputs from 2215(a) . . . (n) are composited by operationmodule “

” 2217 and operations of each algorithm branch and render output 2219.The operator

module 2217 leverages the FLUTTER™ algorithm using apriori knowledge ofthe apparatus and a desired signal as well relationships derived fromthe following variables, functions and parameters:

-   v_(i,l): A set of degrees of freedom ranging from 1 to μ. That is,    -   Here the l^(th) instantiation of the v indices may assume any        combination from the set 1≦μ·i, is a partition number and l may        contain any grouping of partitions.        may operate on these sets and groupings internally.-   i: i^(th) energy partition increment, which can be associated with a    subset of up to v system degrees of freedom.-   {tilde over (η)}_(i): η or suitable function of η in i^(th) path    considering one or more inefficiencies of that path, including the    interacting (compositing) of the v_(i) subsets of degrees of    freedom.-   H(x): Information source (or other suitable representation) input    whose pdf (probability density function) is p(x) (or other suitable    representation).-   H(y): Information output (or other suitable representation) whose    pdf (probability density function) is p(y) (or other suitable    representation).-   X_(n)(t): n^(th) signal sample for ideal reference.-   Y_(n)(t): n^(th) signal sample for system output.

The vector synthesis engine (VSE) module 2203 calculates the per sample,functions for the v_(i), domains supporting functions 2207, 2209, 2211,and 2215. The calculations include apriori knowledge of the apparatusconfiguration and technology characterization. Models considerefficiency and signal space geometries for one or more system states γwhich contemplate, signal type, signal rate, temperature, dynamic range,power supply variation, etc.

FIG. 22 is an operational mixture of functions that illustrate the jointprocessing of signal energy and the associated information metricsencoded into y_(n)(t) 2219 mapping, or blending, or compositing, at theoutput.

Functions/modules 2209 (a . . . n), 2211 (a . . . n). 2215 (a . . . n),2217, 2205 (a . . . n), and 2203, may be implemented by a suitable blendof hardware and software using microprocessor and/other appropriateconfigurable and/or programmable technologies. Also analog technologymay be used to implement these functions with suitable A/D and D/Ainterfaces where applicable to transition between analog and digitalprocessing functions/modules.

As previously indicated R_(xy) or corresponding covariance is a usefulmetric for indirectly assessing S_(J) _(e) , S_(J) _(w) .

|1−|R _(xy) ∥∝kS _(J) _(w)

If this quantity is zero then S_(J) _(e) is maximized and S_(J) _(w) isminimized, as a necessary but not sufficient condition.

Since x and y are complex signals the cross-correlation may also be acomplex number. R_(xy) may therefore also be used to obtain errors forsignal magnitudes and phase. This is necessary and sufficient.

An apparatus that includes multiple technologies operated in nonlinearregions is difficult to model. The complex impulse response consists ofa series of Volterra kernels. FIG. 22 illustrates the Vector SynthesisEngine (VSE) 2203, which generates the intermediate blended controls2211 based on knowledge of the apparatus partitions, desired outputsignal 2219, targeted efficiency vs. signal quality metric, and modeledor characterized nonlinearities, NL₁, NL₂, . . . NL_(i) 2215 (a),2215(b) . . . 2215(n) (where “n” is any suitable number). Models basedon Volterra functional series are usually complex and, therefore,typically difficult to analyze and compensate in hardware for real timeapplication. Rather, embodiments of the present invention are directedto creating an image that provides what may be described as an “entropyflux surface”, or herein after, simply “differential surface”. Thesurfaces (entropy flux surfaces) are extracted as sets of 3-dimensionalcross sections of higher order complex hyper-geometric manifolds. Eachset of surfaces corresponds to a particular state of one or moremodulators plus supporting functions, or collectively the apparatus andeach state is characterized by at least 2 differential surfaces that maybe obtained from a cross-correlation function, or a correspondingcovariance.

FIGS. 23A and 23B are graphics that illustrate an example of thedifferential surfaces for a particular state. Specifically, FIG. 23Ashows a graphical illustration 2300 of a differential magnitude entropysurface 2307 and FIG. 23B shows a graphical illustration 2301 of a phaseentropy surface 2317.

As shown in FIG. 23A, the differential magnitude entropy surface 2307 isplotted on X-axis 2302, Y-axis 2304 and Z-axis 2306. As shown in FIG.23A, the differential magnitude entropy surface 2307 has a substantiallyflat portion 2308 and a substantially conical portion 2310. Thesubstantially conical portion 2310 of the phase entropy surface 2307 isillustrated as being “positive” which is merely a convention choice. Thedifferential surface 2307 could also be represented as “negative”. Also,the designation of the X, Y and Z axes is a convention choice. Anysuitable coordinate system may be used to plot the differentialmagnitude entropy surface. Although surface portion 2310 appears conicalfor this example, it may assume other forms.

FIG. 23B shows a graphical illustration 2301 of a differential phaseentropy surface 2317. This differential phase entropy surface 2317 isplotted on a coordinate space, shown as X-axis 2312, Y-axis 2314 andZ-axis 2316. Differential phase entropy surface 2317 has a substantiallyflat portion 2318 and a substantially conical portion 2320. Thesubstantially conical portion 2320 of the differential phase entropysurface 2317 is illustrated as being “negative” which is merely aconvention choice. The surface 2317 could also be represented as“positive”. Also, the designation of the X, Y and Z axes is a conventionchoice. Any suitable coordinate system may be used to plot thedifferential phase entropy surface. Although surface portion 2320appears conical for this example if may assume other forms.

Sets of such surfaces 2307, 2317 characterize an operational domain of γstates. Surface data are transformed to function coefficients, which maybe further interpolated and extrapolated over the entire set of γstates. This interpolated data feeds the FLUTTER™ algorithm to enablethe creation of Blended Control™ (also known as BLENDED CONTROL BYPARKERVISION™) {tilde over (ℑ)}{H_(v,i)} in concert with the otherparameters previously listed. The process renders new functions thatpossess properties that minimize S_(J) _(w) , production, the result ofwhich is illustrated in FIGS. 24A and 24B.

FIG. 24A shows a graphical illustration 2400 of a reduced differentialmagnitude entropy surface 2408. This reduced differential magnitudeentropy surface 2408 is plotted on X-axis 2402, Y-axis 2404 and Z-axis2406. As shown in FIG. 24A, the reduced differential magnitude entropysurface 2408 has a substantially flat portion. (“Substantially” is usedas a relative term with respect to a quality metric that is a systemdesign parameter.) The designation of the X, Y and Z axes is aconvention choice. Any suitable coordinate system may be used to plotthe differential magnitude entropy surface.

FIG. 24B shows a graphical illustration 2401 of a reduced differentialphase entropy surface 2418. This reduced differential phase entropysurface 2418 is plotted X-axis 2412, Y-axis 2414 and Z-axis 2416. Thereduced differential phase entropy surface 2418 has a substantially flatportion 2420 and a substantially conical portion 2419. The substantiallyconical portion 2419 of the reduced differential phase entropy surface2418 is substantially more narrow (less surface area) than the phaseentropy error conical portion of FIG. 23B. The designation of the X, Yand Z axes is a convention choice. Any suitable coordinate system may beused to plot the differential phase entropy surface.

As shown in FIGS. 24A and 24B, the error metric S_(J) _(w) is reduced tothe lowest acceptable, or lowest compliant, value through {tilde over(ℑ)}{H_(v,i)} while articulating the most efficient resources availablewithin the apparatus to produce S_(J) _(e) . Since nonlinearities in onebranch, as shown in FIG. 22, 2205, may reduce the capacity of thatbranch while enhancing efficiency, another branch makes up thedifference in information capacity. The relative partial informationcapacities and efficiencies of algorithm branches may fluctuatedynamically during compositing. Branch domains may overlap through thesets of {tilde over (ℑ)}{H_(v,i)} even if energy domains (i) may or maynot overlap. Whenever overlap of v₁, v₂, v₃ control domains overlap, thestatistics of the significant pdfs (probability density functions) p_(v)₁ , p_(v) ₂ . . . will possess cross-correlation properties. Thispermits each energy partition (i) to excite v_(μ) controls in parallelwith the proper statistical weighting, thus blending, or compositing,information from {tilde over (ℑ)}{H_(v,i)} domains.

FIG. 25 shows an example of a joint probability space diagram 2500. Asshown in FIG. 25 an output amplitude domain waveform pdf (probabilitydensity function) p(V_(L)) 2506 is generated from {tilde over (ℑ)}{H(p₁,p₂, . . . p_(v))}, which is composite, or blended control, PDFs(probability distribution function). Each member of this composited setis a pdf (probability density function) of a non-stationary randomvariable, which may be continuous, discrete or both (illustrated ascontinuous for example).

As seen in FIG. 25, the solid line 2506 illustrates the composited pdf(probability density function) p_(v)(V_(L)) can be considered as a jointdistribution that is dependent on several subordinate pdfs joint(probability density functions) or joint sub-distributions {tilde over(ℑ)}{p(V₁|V₂, V₃ . . . V_(v))} 2521, {tilde over (ℑ)}{p(V₂|V₁, V₃ . . .V_(v))} 2522, {tilde over (ℑ)}{p(V₃|V₁, V₂, V₄ . . . V_(v))) 2523,{tilde over (ℑ)}{p(V₄|V₁, V₂, V₃ . . . V_(v))} 2525, and {tilde over(ℑ)}{p(V_(v)|V₁, V₂, . . . V_(v-1))} 2526 in this example. The graph2500 is plotted with respect to X-axis 2502 vs. Y-axis 2504. Severaldegrees of freedom (v) were used to form the example statistic shown inFIG. 25. Specifically, 3 energy partitions E₁, E₂, E₃=3, <=2) areillustrated (2516, 2518 and 2520) (without any consideration foroptimization). Notice that the subordinate p_(v) functions 2521, 2522,2523, 2525 and 2526 interact statistically to form a compositerepresentation, shown as line 2506. FIG. 25 provides a statisticaldescription of a representation of an information bearing function oftime. Components of phase, amplitude and frequency are contemplated asextensions of the composited statistic. Hence, the variables possesssome correlation for the region of overlap. This correlation is avariable which is a function of the set of voltages or signals V_(L),{tilde over (ℑ)}{(V₁, V₂, . . . V_(v))}. Also each energy partition2516, 2518 and 2520 may span a subset of the blend from the availablep_(v) _(μ) . In addition, a suitable blend of subordinate joint pdfs ispossible which possess tailored cross covariance.

FIG. 25 shows a 2-dimensional RV; however, the RV is in generalapplicable to any suitable number of complex dimensions. FIG. 25illustrates how an output V_(L) may be a composited result of severalconstituents (V₁, V₂, V₃ . . . V_(v)).

FIG. 26 shows a flow chart 2600 that illustrates a FLUTTER™ algorithmdevelopment approach that considers up to v plus i additionalmacroscopic degrees of freedom for the apparatus. As shown in FIG. 26,the flow chart 2600 begins with start step 2602 having a particular setof FLUTTER™ operational parameters and apriori knowledge of theapparatus characteristics. Energy partitions (i) are chosen, as shown instep 2604 according to input 2602. This selection of a number of energypartitions to partition one or more energy sources depends on a desiredresolution to render a signal or a waveform that can be encoded withinformation (generally referred to herein as an information bearingfunction of time). The (i) partitions may be fixed domain (as shown instep 2606) or fixed plus switch PS domain (as shown in step 2608).

v degrees of freedom are allocated, as shown in step 2610. Theallocation of step 2610 is used for compositing, as well as p_(v)(V_(L))distributions.

Joint optimization of η, H_(x)−H_(y) is performed, as shown in step2614. This joint optimization of step 2614 also is a function of ΔS2612. The result of the joint optimization is analyzed as shown in step2616. This analysis includes checking {tilde over (ℑ)}{

η_(tot)

} and {tilde over (ℑ)}{R_(xy)}. The result of this analysis of step 2616is either acceptable, as shown by reaching step 2630 or rejected, asshown by line 2618, which shows that the optimized blending function isiterated, as shown in step 2620. This optimization may be accomplishedby some combination of characterization, measurement and calculationwhich can be iterative or solved through the calculus of variations. Theresult of the possibly iterative optimization process (2620) is used instep 2610, as shown by line 2615. The result from the iterativeoptimization process (2620) may also be used in the partitioning step2604, as shown by line 2622. Once this optimization is complete, theresulting optimization parameters may be applied in a feed forwardapplication of FLUTTER™. FIG. 26 illustrates a general method forobtaining a statistical characterization of an apparatus supporting theFLUTTER™ algorithm which utilizes the characterization as prior systemknowledge and apriori knowledge

For many applications it is advantageous to reduce individual FLUTTER™domain sample rates and dynamic ranges, particularly if a switched orswitching power supply is utilized in one or more than one of the energypartitions.

The number of signal samples per energy partition can be approximatelyobtained from;

n_(i) = λ_(i)2 W τ n_(i_(ma x)) = λ_(i_(ma x))2 W τn_(i_(m i n)) = λ_(i_(m i n))2 W τ$\frac{n_{i_{m\; i\; n}}}{2{\tau\lambda}_{i_{m\; i\; n}}} \leq W_{i} \leq \frac{n_{i_{{ma}\; x}}}{2{\tau\lambda}_{i_{{ma}\; x}}}$

The sampling rate for the i^(th) can then be given by 2 W_(i), whereW_(i) is the required bandwidth of joint FLUTTER™ processes in i^(th)partition, although there is a finite probability of switching betweenany of the domains from sample to sample, the averaged switch frequencyon a per domain basis is given by;

R _(i)=λ_(i) R _(sx)≦2W _(i)

where R_(sx) is the maximum switch rate, and λ_(i) is a suitable ratemultiplier.

This rate can be further reduced by redistribution of or suitabledistribution of, the frequency components of the FLUTTER™ blendedcontrols. Additional amplitude and phase information not accommodated byswitching power supply or switched power supply control is allocated tothe v remaining degrees of freedom. These parallel paths permit the fulldynamic range and resolution of the signal to be reconstructed “on thefly”, sample by sample, using the VSE (Vector Synthesis Engine) moduleto optimize

η

and R_(xy).

The amplitude modulations are partially instantiated by the energydomain control at each V_(s) _(i) boundary. Additional amplitude controlis facilitated in the v remaining degrees of freedom (as shown by step2610) for the modulator device.

It is helpful to describe embodiments of the present invention using avariety of general topologies, which incorporate FLUTTER™ for amodulator. FIG. 27 shows an example of FLUTTER™ with (i) partitions andv auxiliary degrees of freedom. Indeed, FIG. 27 shows one topology 2700related to d2p™ application with Type I modulation properties.

The embodiment shown in FIG. 27 shows an example of one embodiment 2700of the present invention. FIG. 27 shows energy sources V_(s) ₁ , V_(s) ₂. . . V_(s) _(i) 2708 (a), 2708(b) and 2708(n), respectively) where “n”is any suitable number. It is an embodiment of the present inventionthat any suitable number of energy sources may be used. Althoughillustrated as DC batteries for this example, it is understood that theenergy sources may possess any statistic of voltage or current and mayalso be encoded with information. Blended controls, {tilde over(ℑ)}{H(x)_(v,i)} 2702 are generated from a VSE (Vector SynthesisEngine), as described herein. A portion 2702(a) of the control function2702 is provided to a switching control to selectively access one of theenergy sources (generally 2708) connection as shown by 2711, 2709 and2713. The switch contact, 2709 and connection nodes 2713 (a . . . n) areactivated based on the control signals of 2702(a) and switch control2711. The selected energy source of the plurality of sources (generally2708) provides energy, in any suitable form, which may include voltage,current, excitation or other stimulus to impedance module −Z_(s) 2789.

A second portion of blended control, 2702 is 2702(b), which is providedto LO (local oscillator) 2710, which then provides input to modulatormodule 2766. The modulator module 2766 may be, for example a MISO(multiple input single output module). The matching impedance 2769receives the interaction of Z_(s) 2789-modulator module 2766, and thesources 2708(a) . . . (n). V_(L) Δy(t) 2774 is rendered at load 2764. Inthis example, the energy sources 2708 (generally) are partitionedaccording to control signals 2702(a), which partition the energy samplesinto a number of partitions, which can be enumerated as i≦2^(k) where kis the resolution used for reconstructing the signal amplitude and/orphase typically i<<k for fixed partitions. Indeed, it is contemplatedthat i may be a suitable integer of fixed partitions to obtain adesirable efficiency. For example i could be an integer such as 2 andoffer performance advantage (compared to legacy technologies) in therendered output signal V_(L) 2774 at load R_(L) 2764. In this example,none of the partitions require switching power supplies. Switching powersupplies may also be used. The additional v dimensions provide forcomplex signal reconstruction, or rendering, of both desired magnitudeand phase at the output 2774 given the constraint of the i^(th) energypartition. FIG. 28 shows the Thévenized equivalent of FIG. 27.

In FIG. 28, the embodiment shown as 2800 shows that the several voltagesof FIG. 27 are replaced by the parallel combination of I_(i) and Z_(i).These combinations of I_(i) and Z_(i) are shown as pairs 2818, 2819;2820, 2821; and 2822, 2823. Current is provided to Z_(s) 2889 as afunction of control signals, such as FLUTTER™ blended control signals,2802, which includes 2802(a) and 2802(b). A portion (2802(a)) of thecontrol function 2802 is provided to a switching control to selectivelyaccess one of the pairs (2818, 2819; 2820, 2821; 2822, 2823) as shown by2813 and 2811. This selective access is shown as element 2807. Theconnections 2815, 2813 and 2811 are activated based on the controlsignals of 2802(a). The selected energy source of the plurality ofsources provides energy, in any suitable form, which may includevoltage, current, power or any other excitation force to impedancemodule Z_(s) 2889. Although illustrated as a generic current sources forthis example, it is understood that the energy sources may possess anystatistic of current and may also be encoded with information (portionof H(x)).

A second portion of control, or FLUTTER™ blended control function 2802is 2802(b), which is provided to LO (local oscillator) 2810, which thenprovides input to a modulator module which may be for example a MISO2866.

Also, a portion of the control signals from 2802 may also be provided toa modulator module which may be for example a MISO 2866.

The modulator module 2866 may be, for example a MISO (multiple inputsingle output module). The matching impedance 2869 receives the outputfrom Z_(s) 2889 and the interaction of modulator module 2866 rendersV_(L) 2874 at load 2864.

Similar to the embodiment described in relation to FIG. 27, the energysources of FIG. 28 are partitioned according to control signals 2802(a),which partition the energy sample into a number of partitions, which canbe explained as i≦2^(k) where k is the resolution used forreconstructing the signal amplitude and/or phase. Typically i<<k forfixed partitions. Indeed, it is contemplated that i may be a suitableinteger based on the available resources desired efficiency and signalquality as well cost of implementation, to obtain a desirableefficiency. For example i may be an integer such as 2 and offerperformance advantage.

FIG. 29 shows an embodiment 2900 of the present invention. FIG. 29accommodates variable switching power supplies for one or more of thepartitions. As shown in FIG. 29, power supplies 2908(a) . . . (n) (where“n” is any suitable number) receive a first portion of control signals2902(a). For example, the power supplies (generally 2908) receivecontrol signals 2902(a). Switching of switch 2909, is controlled byswitch control 2911 via some portion of the signals 2902(a). Onceselected a power source 2908 (a) . . . (n) provides energy to Z_(s) 2989as well as other portions of 2900.

A second portion of the control function signals 2902(b) is provided tomodulator module, which may be, for example a MISO (multiple inputsingle output module) 2966 and LO (local oscillator) 2910. The modulatormodule 2966 power source interacts with circuit impedances Z_(s) 2989,Z_(m) 2969, R_(s) 2964, LO 2910, switch 2909, power sources 2908 (a . .. n) and controls 2902 to generate an output V_(L) 2974.

The architecture shown in FIG. 29 represents nesting of partitionswithin partitions. Each of the (i) partitions 2902 may be separatelysubdivided into partitions that can be implemented by a variable, orswitching, power supply. Controls 2902 (c . . . n) provide a means ofadjusting energy source voltages 2908 (a . . . n) within a selectedpartition. One or more of the (i) partitions can be realized in thismanner. Depending on the specific partitions,

η

may be increased while providing finer control of amplitudereconstruction over some portion of the envelope dynamic range. Anydomain not controlled by a switching power supply may be supplied by afixed source (source with a significantly constant describing pdf forvoltage or current). A Thévenized architecture may replace the variable,or selectable, voltage sources.

Alternative strategies may be presumed for power supply partitioning.This consideration may be applied to any architecture employingFLUTTER™.

FIG. 30 shows an alternate embodiment 3000 of the present invention. Asshown in FIG. 30, the embodiment 3000 presents the power sourcecascading, alternative. Portions of the control function signals 3002(3002(a) and 3002 (b)) are provided to energy sources 3008 (a) . . . (n)(where “n” is any suitable number) and to modulator module 3066 as wellas LO 3010. The energy sources (generally 3008) may provide voltage,current, power, or any other suitable excitation waveform or energy ofany suitable statistic to Z_(s) module 3089 via controlled switchingmechanisms 3011 and 3009. Node 3062 is also shown. Node 3062 is a nodewhich possesses a composite signal statistic.

A signal generated at node 3062 from the interaction of 3066, and 3089,3009, as well as 3008 is also provided to Z_(m) 3069, which is thenprovided to the load 3064, to render V_(L) 3074.

The structure may also be Thévenized. In addition, both series andparallel power sources can be utilized in place of the fixed seriespower source bank. Also, as an alternative embodiment, none of the powersupplies may be variable or any subset may be variable. Variablesupplies are typically switching power supplies, or other equivalentlyefficient technology.

FIG. 31 illustrates another embodiment 3100 of the invention. 3100 is amodulation architecture which supports the FLUTTER™ algorithm. Thisstructure 3100 may also be referred to as a Type 3 modulator. 3100 maybe instantiated one or more times to support complex baseband or passband modulations.

3101 is any suitable energy source consisting of up to 2(i+1) distinctsources and associated branches which may possess currents which haveD.C., A.C. characteristics or both. The voltages +/−V_(s) ₁ 3102,+/−V_(s) ₂ 3103 up to +/−V_(i+1) 3104 where i+1 is some suitable integersupporting up to i partitions, along with the voltages −/+{circumflexover (V)}_(s) ₁ 3105, −/+{circumflex over (V)}_(s) ₂ 3106 up to−/+{circumflex over (V)}_(i+1) 3107 are supplied by module 3101.

Impedance Z₁, 3108, is allocated to the circuit branch associated with+/−V_(s) ₁ 3102. Impedance Z₂, 3109 is allocated to the circuit branchassociated with +/−V_(s) ₂ 3103. Impedance Z_(i+1) 3110 is allocated forthe circuit branch associated with the voltage +/−V_(s) _(i+1) 3104 inthe (i+1)^(th) power supply branch. Impedance {circumflex over (Z)}₁3111, is allocated to the circuit branch associated with −/+{circumflexover (V)}_(s) _(i) 3105. Impedance {circumflex over (Z)}₂ 3112 isallocated to the circuit branch associated with −/+{circumflex over(V)}_(s2) 3106. Impedance {circumflex over (Z)}_(i+1) 3113 is allocatedto the circuit branch associated with −/+{circumflex over (V)}_(s)_(i+1) 3107.

Switch or Commutator 3114 accesses voltages +/−V_(s) ₁ 3102, +/−V_(s) ₂3103 . . . +/−V_(s) _(i+1) 3104 after interaction with impedances Z₁,3108, Z₂, 3109, up to and including Z_(i+1) 3110.

Switch or Commutator 3115 accesses voltages −/+{circumflex over (V)}_(s)₁ 3105, −/+{circumflex over (V)}_(s) ₂ 3106 . . . −/+{circumflex over(V)}_(s) _(i+1) 3107 after interaction with impedances {circumflex over(Z)}₁, 3111, {circumflex over (Z)}₂ 3112, up to and including{circumflex over (Z)}_(i+1) 3113.

Switches or commutators 3114, 3115 are controlled via function 3119which is a subset of blended controls {tilde over (ℑ)}{H(x)_(v,i)}distributed from a VSE 3121.

Z_(L) 3118 Load Impedance develops a differential output voltage V_(L)3122 according to currents flowing in the circuit determined by selectedpower sources, voltages +/−V_(s) ₁ 3101, +/−V_(s) ₂ 3103 . . . +/−V_(s)_(i+1) 3104, voltages −/+{circumflex over (V)}_(s) ₁ 3105,−/+{circumflex over (V)}_(s) ₂ 3106 . . . −/+{circumflex over (V)}_(s)_(i+1) 3107 as well as impedances Z₁ 3108, Z₂ 3109, . . . Z_(i+1) 3110,impedances {circumflex over (Z)}₁ 3111, {circumflex over (Z)}₂ 3112 . .. {circumflex over (Z)}_(i+1) 3113, impedance Z_(Δ)/2 3116, impedance{circumflex over (Z)}_(Δ)/2 3117, and Z_(L) 3118.

This modulator topology can deliver unipolar, bipolar, balanced orunbalanced signals, V_(L) 3122 across the load Z_(L) 3118 depending onthe choice of supply voltages and their relative average values withrespect to some system reference potential. A fully differential andbalanced output with an average of zero volts at V_(L) 3122 improvesefficiency.

The impedances Z_(Δ)/2 3116 and {circumflex over (Z)}_(Δ)/2 3117 can beimplemented with transistors or other suitable structure including MISOfunctions conveying trans-impedances which may be modeled as Z_(Δ)/23116 and {circumflex over (Z)}_(Δ)/2 3117.

A Type 4 modulator may be implemented by adding Z_(Δ) _(s) 3125 a shuntimpedance used across the Z_(L) 3118 load impedance terminals andcontrolled by a subset of blended control 3119.

Impedances Z₁ 3108, Z₂ 3109, up to and including Z_(i+1) 3110 as well as{circumflex over (Z)}₁ 3111, {circumflex over (Z)}₂ 3112 up to andincluding {circumflex over (Z)}_(i+1) 3113 are partially reflective ofsource power supply parasitic impedances. However, these impedances maybe augmented with reactive components to assist in the reconstruction ofanalytic signal envelopes from circuit currents and voltages.

The modulator structure 3100 of FIG. 31 may be embedded in FIG. 14 toimplement complex modulation schemes. The variable or switched energy orpower source module 3123 may be deployed in part or whole to modules1420 and 1430 of FIG. 14. Also, module 3124, the variable impedancemodule, may be deployed in part or whole to module 1460 of FIG. 14 aspart of the

operator. It should also be noted that controls 3119 correspond to somesubset of the controls 1401 of FIG. 14.

While a Type 3 modulator requires variable impedances Z_(Δ)/2 3116,{circumflex over (Z)}_(Δ) _(s) /2 3117 is considered optional. A Type 4modulator utilizes the shunt impedance Z_(Δ) _(s) /2 3125.

The switching and/or switched power supply sources may consist of up to2(i+1) discrete fixed/constant power sources or up to 2(i+1) variablepower sources, or a mix of constant and variable types. The powersources may be current sources or voltage sources. The characteristicsand values associated with each power source giving rise to voltages+/−V_(s) ₁ 3102, +/−V_(s) ₂ 3103 . . . +/−V_(s) _(i+1) 3104,−/+{circumflex over (V)}_(s) ₁ 3105, −/+{circumflex over (V)}_(s) ₂ 3106. . . −/+{circumflex over (V)}_(s) _(i+1) 3107, are selected andcontrolled via a subset of blended controls 3119 distributed from a VSE3121 by suitable analog or digital means.

The power spectral density (psd) of each blended control may be unique.The psd of each blended control may be dynamic and a function of time orstate of 3100.

The rates and/or bandwidths of each blended control may be tailored toselect or adjust each switch, function, or impedance to reconstruct adesired signal V_(L) 3122 according to some desired metric. The ratesand/or control bandwidths are distributed to maximize apparatusefficiency while conserving H(x) some desired information entropyconveyed through the system to produce V_(L) 3122.

In general, each function block of 3100 may possess unique referencevoltages which are distributed to internal circuit nodes of theindicated or associated impedances or functions. The reference voltage,V_(ref) _(_) _(sys) 3140, is associated with 3101, switching and/orswitched power supply sources. Reference voltage V_(ref) ₁ 3130 isassociated with Z₁ 3108. Reference voltage V_(ref) _(z) 3131 isassociated with Z₂ 3109. Reference voltage V_(ref) _(i+1) 3132 isassociated with Z_(i+1) 3110. Reference voltage {circumflex over(V)}_(ref) ₁ 3133 is associated with {circumflex over (Z)}₁ 3111.Reference voltage {circumflex over (V)}_(ref) _(z) 3134 is associatedwith {circumflex over (Z)}₂ 3112. Reference voltage {circumflex over(V)}_(ref) _(i+1) 3135 is associated with {circumflex over (Z)}_(i+1)3113. Reference voltage V_(ref) _(Δ) 3136 is associated with Z_(Δ)/23116.

Voltage Reference {circumflex over (V)}_(ref) _(Δ) 3137 is associatedwith {circumflex over (Z)}_(Δ)/2 3117.

Voltage Reference

V_(ref_(Δ_(S)))3138

3138 is associated with Z_(Δ) _(s) 3125.

Voltage Reference V_(ref) _(out) 3139 is associated with Z_(L) 3118.

In general the reference voltages for the impedances and functions ofcircuit 3100 may possess differing values. The reference voltages maypossess the same values. The reference voltages may be zero or any othersuitable value. The choice of reference voltages will depend on the biasrequirements for each circuit impedance or function, the interfacerequirements for connected circuits or functions and the requirement toimplement waveform or signal offsets within 3100.

Blended control Distribution 3121 provides blended controls {tilde over(ℑ)}{H(x)_(v,i)} 3119 to various functions and impedances within 3100.The controls 3119 may be digital, analog or a mix of both. Each controlpath is labeled with a dimension indicating the number of unique controlsignals allocated to the indicated path. k_(ps) 3150 is a number ofcontrols less than or equal to 2(v+i) and associated with the switchingand/or switched power supply sources 3101. k_(sx) 3152 is a number ofcontrols less than or equal to v+i, and associated with switch 3114.

3151 is a number of controls less than or equal to v+1, and associatedwith switch 3115. k_(Z) _(Δ) is a number of controls less than or equalto v+1, and associated with variable impedance Z_(Δ)/2 3116.k_({circumflex over (Z)}) _(Δ) is a number of controls less than orequal to v+i, and associated with variable impedance {circumflex over(Z)}_(Δ)/2 3117. k_(Z) _(Δs) is a number of controls less than or equalto v+1, and associated with variable impedance Z_(Δ) _(s) 3125. Thenumber of control signals may or may not correspond exactly to thenumber of physical connections in each control path at each functioninterface. Controls may be distributed serially or otherwise distributedor multiplexed on a common connection, wire, or path.

Another embodiment 3200 of the invention is illustrated in FIG. 32. 3200is a general modulation architecture capable of supporting FLUTTER™algorithms. 3200 can create virtually any signal in an efficient mannerwhen operated in conjunction with the FLUTTER™ algorithm.

V_(S_(U₁))3201, V_(S_(U₂))3202,

up to and including

V_(S_(U_(i)))3203,

are variable voltage or current sources associated with upper branchmodulator 3227.

V_(S_(L₁))3204, V_(S_(L₂))3205,

up to and including

V_(S_(L_(i)))3206

are variable voltage or current sources associated with the lower branchmodulator 3228. Collectively these sources are controlled via blendedcontrols distributed through digital and/or analog methods from a VSE3219. Collectively the voltage and/or current sources

V_(S_(U₁))3201, V_(S_(U₂))3202,

up to and including

V_(S_(U_(i)))3203

are referred to as upper branch sources. Collectively, the voltageand/or current sources

V_(S_(L₁))3204, V_(S_(L₂))3205

up to and including

V_(S_(L_(i)))3206

are referred to as lower branch sources. The upper branch sources andlower branch sources may be composed of any combination of current andvoltage sources. The upper branch sources and lower branch sources maybe D.C., A.C., or mixed and possess any suitable statistic of voltagesor currents. The upper branch sources and lower branch sources may beharmonic functions or modulated harmonic functions. The upper branchsources and lower branch sources may be random. The upper branch sourcesand lower branch sources may possess both harmonic and random waveformmetrics as may be required. The fundamental frequency of each of theupper branch sources and each of the lower branch sources may beindependently varied from 0 Hz (D.C. case) to any suitable upperfrequency limit. The phase of each of the upper branch sources and eachof the lower branch sources may be independently varied from 0° degreesto modulo 360° degrees as required. The amplitudes for each of the upperbranch sources and each of the lower branch sources may be independentlycontrolled as required.

Z_(U) ₁ 3207 is a variable impedance associated with voltage or currentsource

V_(S_(U₁))3201.

Z_(U) ₂ 3208 is a variable impedance associated with voltage or currentsource

V_(S_(U₂))3202

up to and including Z_(U) ₁ 3209 variable impedances are associated withup to and including

V_(S_(U_(i)))3203

voltage or current sources.

Z_(L) ₁ 3210 is a variable impedance associated with voltage or currentsource

V_(S_(L₁))3204.

Z_(L) ₂ 3205 is a variance impedance associated with voltage or currentsource

V_(S_(L₂))3211

up to and including Z_(L) _(i) 3212 variable impedances are associatedwith up to and including

V_(S_(L_(i)))3206

voltage or current sources.

Collectively Z_(U) ₁ 3207, Z_(U) ₂ 3208 up to and including Z_(U) _(i)3209 variable impedances are referred to as upper branch sourceimpedances. Collectively Z_(L) ₁ 3210, Z_(L) ₂ 3211, up to and includingZ_(L) ₁ 3212 variable impedances are referred to as lower branch sourceimpedances.

A variable portion of each upper branch impedance and each lower branchimpedance are controlled via a subset of blended controls 3220distributed by digital and/or analog means from a VSE 3219.

The index value i enumerating the upper branch sources, upper branchsource impedances, lower branch sources, and lower branch sourceimpedances, may assume any suitable integer value.

An upper branch commutator or switch 3213 selects an upper branch sourcevia an associated upper branch source impedance based on a subset ofblended controls 3220. A lower branch commutator or switch 3214 selectsa lower branch source via an associated lower branch source impedancebased on a subset of blended controls 3220.

The selected upper branch commutator or switch 3213 output 3222 isrouted to variable upper branch impedance Z_(Δ) _(U) 3215. The selectedlower branch commutator or switch 3214 output 3225 is routed to variablelower branch impedance Z_(Δ) _(L) 3216.

Z_(Δ) _(U) 3215 and Z_(Δ) _(L) 3216 variable upper branch and lowerbranch impedances respectively are controlled by a subset of blendedcontrols 3220 distributed by digital and/or analog means from a VSE3219.

An output 3222 from variable upper branch impedance Z_(Δ) _(U) 3215 isrouted to output compositing Function 3217 also labeled as

. An output 3223 from variable lower branch impedance Z_(Δ) _(L) 3216 isrouted to output compositing Function 3217 also labeled as

.

Output Compositing Function 3217 operates on inputs 3222 and 3223 tocreate output composited signal V_(L) 3226 at load impedance Z_(L) 3218.Control/s 3221 varies of the output Compositing Function 3217 accordingto a subset of blended controls 3221.

The upper branch modulator 3227 and lower branch modulator 3228 alongwith blended controls 3220 and 3221 distribution of suitable preparedcontrols from the VSE 3219 and Compositing Function 3217, include auniversal modulator generating virtually any modulated waveform/signalat V_(L) 3226, over frequency spans from baseband to any suitablecarrier frequency. Furthermore, blended controls 3220, 3221, may be atsuitable rates to support desired signal data rates and bandwidths, anysignal path as well as at the output V_(L) 3226.

Each upper branch source, each lower branch source, each upper branchsource impedance, each lower branch source impedance, variable upperbranch impedance, variable lower branch impedance as well as compositingfunction may possess independent controls with independently variableinformation control rates and/or bandwidths.

A certain portion of information entropy H(x) distributed as a functionof apparatus degrees of freedom and partitions. {tilde over(ℑ)}{H(x)_(v,i)} is distributed via blended controls 3220, 3221, to eachvariable functions and modules comprising 3200.

As a consequence, a differing portion of information entropy H(x) issupported or conveyed by each variable function or module of 3200 suchthat an output compositing function 3217 conserves input informationentropy H(x) at the output V_(L) 3226 albeit in a signaling format ofchoice which may be for example a modulated RF carrier signal. Eachvariable function or module of 3200 is assigned some portion of theinput entropy H(x) based on the portion of the originating informationdescribing probability density function p(x) which exploits the mostefficient modes of the apparatus. That is, an original density functionp(x) with associated information entropy H(x) may be parsed to a set ofjoint probability densities p(x)_(v,i) each with associated entropiesH(x)_(v,i) which may be independent or partially correlated. The mannerin which the set p(x)_(v,i) is defined is based on a maximization ofdistributed apparatus efficiency (and hence total efficiency) and therequirement to conserve H(x) in the modulation process.

For example, for a particular application of 3200 it may be efficient torestrict the rate at which the upper branch sources and lower branchsources may be varied. Amplitudes may be fixed or slowly varied at onesample rate of bandwidth. Phases may be varied at differing rates whichare more rapidly varying than amplitudes of the sources. The upperbranch source impedances and lower branch source impedances may vary atunique rates. The commutator or switch 3218, 3214 selection rates may beunique. The variable upper branch impedance 3215 and the variable lowerbranch impedance 3216 may vary at unique rates. Operations within theoutput compositing function 3217 may vary at unique rates. Each blendedcontrol may possess an associated unique power spectral density (psd).Each blended control may possess a power spectral density that varies.In this manner the output modulation of signal V_(L) 3226 is acomposited blend of functions within the apparatus which are optimizedaccording to control rate vs. efficiency and dynamic range vs.efficiency per function or module. The total efficiency is the averageefficiency for all functions or modules of 3200 operating in concert.

In general, each unique desired output signal statistic may utilize newrates for all functions and modules and redefine the set p(x)_(v,i)which in turn modifies the weighting of the blended controls {tilde over(ℑ)}{(H(x)_(v,i)}.

All degrees of freedom illustrated in FIG. 32 may not be required forevery application. For instance, some applications may not require upperbranch source impedances which vary and lower branch source impedanceswhich vary. In some circumstances upper branch source frequency andlower branch source frequency may be fixed. Logical redaction isapparent to those skilled in the art.

It is also apparent that either the upper branch modulator 3227 or lowerbranch modulator 3228 may function as modulators separate from oneanother provided they benefit from suitable blended controls 3220, 3219and output compositing function 3217.

The output compositing Function 3217 is a specific portion of adistributed compositing function. Most generally, compositing is adistributed function embedded in the blended control attributes, in theform of rates relative sample weighting and nonlinear mappings. However,the operator

possesses a prominent position in the modulator signal processing flowand final entropy reconstruction and thus is also referred to as anoutput compositing function in this topology. More specifically, it is afinal mapping in the compositing process which constructs the desiredoutput signal whilst conserving H(x).

There are the following reference voltages which may be associated withinternal circuit nodes for the associated impedances and functions whichare subordinate to 3200.

Reference Voltage ref_u₁ 3230 is associated with Z_(U) ₁ 3207.

Reference Voltage ref_u₂ 3231 is associated with Z_(U) ₂ 3208.

Reference Voltage ref_u_(i) 3232 is associated with Z_(U) _(i) 3209.

Reference Voltage ref_L₁ 3233 is associated with Z_(L) ₁ 3210.

Reference Voltage ref_L₂ 3234 is associated with Z_(L) ₂ 3211.

Reference Voltage ref_L_(i) 3235 is associated with Z_(L) _(i) 3212.

Reference Voltage ref_Δ_(U) 3236 is associated with Z_(Δ) _(U) 3215.

Reference Voltage ref_Δ_(L) 3237 is associated with Z_(Δ) _(L) 3216.

Reference Voltage ref_

_(U) (3238) is associated with output Compositing Function (3217).

Reference Voltage ref out 3239 is associated with output load Z_(L)3218.

The above listed reference voltages may assume any suitable value fordistribution to circuit nodes internal to the associated impedances orfunctions. The reference voltages may or may not be equal. The referencevoltages may or may not be zero. The choice of reference voltage foreach function or impedance depends on whether the functions impedancesrequire some particular operational bias voltage to implement arespective function, facilitate interface to connected impedances orfunctions, or to implement waveform or signal offset values.

In general each circuit internal to the impedances Z_(U) ₁ 3207, Z_(U) ₂3208, up to and including Z_(U) _(i) 3209, Z_(L) ₁ 3210, Z_(L) _(z) 3211up to and including Z_(L) _(i) 3212, Z_(Δ) _(U) 3215, Z_(Δ) _(L) 3216and Z_(L) 3218 may possess series and shunt circuit elements withrespect to input, output, and reference voltage terminals as well as anydefined system ground potential. Likewise, output compositing function

may consist of series and shunt circuit elements with respect to input,output, blended control and reference voltage ref_

3238 voltage terminals as well as any defined system ground potential.

Blended controls 3220 and 3221 distributed from VSE 3219 consist of theillustrated control paths from 3219 to each respective applicablefunction within 3200. Each illustrated control path is assigned adimension labeled k₁ 3240, k₂ 3241, k₃ 3242, k₄ 3243, k₅ 3244, k₅ 3245,k₇ 3246, k₈ 3247, k₉ 3248. Each dimension can assume a number less thanor equal to the number v+i the total number of control degrees offreedom. Each of the dimensions k₁, k₂ k₃, k₄, k₅, k₆ k₇, k₈k₉, may beunique. The dimension values indicate the number of control signalsassigned to each control path. Each control path is some subset of theblended controls 3220, 3221. The number of control signals per path mayor may not correspond to the number of physical connections between thedistribution interface of the VSE 3219 and the respectively connectedfunction within 3200. Each control path may support a number of signalsdifferent than the number of physical path connections throughtechniques of serial control, parallel control, as well as multiplexingor a mixture of these techniques.

Control path dimension k₁ 3240 is associated with Z_(Δ) _(U) 3215.

Control path dimension k₂ 3241 is associated with Switch (3213).

Control path dimension k₃ 3242 is associated with Impedances Z_(U) ₁3207, Z_(U) ₂ 3208 . . . Z_(U) _(i) 3209.

Control path dimension k₄ 3243 is associated with Power Sources

V_(S_(U₁))3201, V_(S_(U₂))3202  …  V_(S_(U_(i)))3203.

Control path dimension k₅ 3244 is associated with Power Sources

V_(S_(L₁))3204, V_(S_(L₂))3205  …  V_(S_(L_(i)))3206.

Control path dimension k₆ 3245 is associated with Impedances Z_(L) ₁3210, Z_(L) ₂ 3211 . . . Z_(L) _(i) 3212.

Control path dimension k₇ 3246 is associated with Switch 3214.

Control path dimension k₈ 3247 is associated with Z_(Δ) _(L) 3216.

Control path dimension k₉ 3248 is associated with output compositeFunction 3217 also on occasion referred to as operator

.

FIG. 33 illustrates a graphic (3300) depicting an example compositedsignal 3301 along with 2 constituent signals, constituent signal (a)3302 and constituent signal (b) 3303. Each of the illustratedconstituents, 3302 and 3303, may also be a composite of otherconstituents, not illustrated.

The constituent signals (a and b) 3302 and 3303 are used as a part of astreamlined example to illustrate several aspects of FLUTTER™ aspertains to the use of blended controls which manipulate architecturessuch as the kind illustrated in FIGS. 1, 2, 3, 4, 13, 14, 18, 22, 26,27, 28, 29, 30, 31 and 32.

Constituent signals (a) 3302 and (b) 3303 are obtained from subsets ofblended controls {tilde over (ℑ)}{H(x)_(v,i)} which shall be labeled{tilde over (ℑ)}{H(x)_(v,i)}_(a) for subset (a) corresponding toconstituent signal (a) 3302 and {tilde over (ℑ)}{H(x)_(v,i)}_(b) subset(b) corresponding to constituent signal (b) 3303. {tilde over(ℑ)}{H(x)_(v,i)}_(a), {tilde over (ℑ)}{H(x)_(v,i)}_(b) may also bereferred to as domains of blended controls or simply as Domainsdepending on context.

Graphic 3301, example output composite, is a desired output signal. Itmay also represent an amplitude envelope for the amplitude modulatedportion of an RF carrier modulated signal, where the carrier wave hasbeen omitted for convenience of illustration. Signal 3301 thereforepossesses the associated desired information entropy H(x). Signal 3302possesses some information entropy H_(a)(x) which is less than H(x).Signal 3303 likewise possesses some information entropy H_(b)(x) whichis less than H(x). The output composite of constituent signal (a) (3302)and constituent signal (b) (3303) is obtained through an operator, sayfor example operator

, which reconstitutes H(x)={tilde over (ℑ)}{H_(a)(x), H_(b)(x)} subjectto some time domain signal requirement, in this case the illustratedsignal 3301.

Close examination of constituent signal (a) 3302 reveals an apparentbandwidth different than the final composite 3301. This signal 3302possesses less than half the bandwidth of signal 3301 for purposes ofillustration, and this specific example.

Examination of constituent signal (b) 3303 reveals an apparent bandwidthon the order of the output signal 3301.

Thus, the effective bandwidth and/or sample rate for {tilde over(ℑ)}{H(x)_(v,i)}_(a) may be different than {tilde over(ℑ)}{H(x)_(v,i)}_(b). This can represent an advantage for casesinvolving apparatus hardware functions which possess varying degrees ofperformance limitations as a function of sample rate and/or bandwidth.Both efficiency and information entropy conservation may be tailored assample rate requirements and bandwidth requirements increase, ordecrease. By distributing the information H(x) into entropies H_(a)(x)and H_(b)(x) the constituent probability densities {p_(a)(x)}_(v,i) and{p_(b)(x)}_(v,i) may be tailored to match the degrees of freedomavailable in the apparatus, allocating information amongst these degreesof freedom to optimize efficiency, and permit conservation of H(x) inthe output signal complex envelope.

In this simple example the composite output signal 3301 is a simple sumof constituent (a) 3302 and constituent (b) 3303 to facilitatedisclosure. That is, the output operator

is linear in this simplified example. In general this may not be thecase and

example may be a more intricate nonlinear function of its inputconstituents. Moreover, the

output operator may possess more than two input constituents. Theconstituent signals associated with {tilde over (ℑ)}{H(x)_(v,i)}_(a) and{tilde over (ℑ)}{H(x)_(v,i)}_(b) may be optional inputs to the outputcompositing procedure on occasion referred to as

. In general {tilde over (ℑ)}{H(x)_(v,i)}_(a) and {tilde over(ℑ)}{H(x)_(v,i)}_(b) may be regarded as nonlinear functions.

It should be noted that if composite output signal 3301 represents anoutput envelope or a signal derived from a complex envelope, that theconstituent signals (a) 3302 and (b) 3303 do not follow the envelope of3301. This is in contrast to envelope following and envelope restorationtechnologies which strive to follow the envelope as accurately aspossible. FLUTTER™ relaxes the requirement for signal processingfunctions such as switching power supplies, for example, to possessextreme instantaneous dynamic range in concert with bandwidth. As anexample consider that some portion of {tilde over (ℑ)}{H(x)_(v,i)}_(a)is allocated to a variable power source. Then to some extent constituentsignal (a) 3302 may be formed from the variation of such a variablepower source. Such a power source may vary without explicitly trackingthe output signal envelope while enhancing efficiency. In contrast 3303may possess a single power supply partition to facilitate {tilde over(ℑ)}{H(x)_(v,i)}_(b) processing for this example. The allocation of ienergy partitions to certain processing domains depends on theefficiency of functions available to those domains vs. the linearityrequirements (capacity to conserve information) associated with thoseprocessing functions. Therefore, in this simplified example it isplausible to allocate i=1 or some other relatively low index for thenumber of energy partitions to process constituent signal (b) 3303 ascompared to the number of energy partitions allocated to processconstituent signal (a) 3302.

Constituent signal (a) 3302 and constituent signal (b) 3303 arecharacterized by random variables with probability density functions.These constituents are subordinate to the composite output signal 3301.The three signals possess differing power spectral densities. Inaddition, constituent signals subordinate to constituent (a) 3302 andconstituent signals subordinate to constituent signal (b) 3303 maypossess differing power spectral densities. FLUTTER™ trades efficiencyvs. processing bandwidth and spectral characteristics according to thesustainable efficiency vs. information throughput for each function ofthe apparatus.

Linearity is not required for each function nor is it necessarilypreferred. Rather efficiency is preferred, metering, subordinate signalsapproximately through nonlinearities such that the compositing processreconstitutes a desired signal without waste or distortion. Undesirablequalities of nonlinear processing are effectively suppressed at thecomposited output signal 3301 exploiting algorithm symmetries, nonlineardiscrimination techniques as well as filtering. Thus, the FLUTTER™technology and philosophy significantly contrast with pre-distortiontechnologies which strive to correct all system nonlinearities. FLUTTER™accentuates the prominence and role of certain classes of nonlinearitiesrather than eliminating them.

FIG. 34 illustrates an example composite output signal 3401 which is thesame as for the example of FIG. 33. Graphic 3402 illustrates a waveformcorresponding to switched voltages of a variable or switched powersource. For example this graphic could be associated with one or moreoutputs of function/module 3101 in FIG. 31. In general it may apply toany power source for FIGS. 1, 2, 3, 4, 14, 18, 22, 26, 27, 28, 29, 30,31 and 32.

Notice the discrete voltage levels depicted in 3402. These levels maycorrespond to i energy partitions which are selected by commentator orswitch functions similar to 3116 and 3117 of FIG. 31 for example. It isapparent after reviewing 3401 and 3402 that the switched voltage powersources 3402 do not track the example composite output signal 3401. Yet,the switched power sources 3402 signal/waveform are used to reconstruct3401. Indeed a portion of the composite output signal 3401 informationentropy is captured in the describing pdf for 3402. It is also apparentthat the average sample rate for 3402 is noticeably less than therequired Nyquist sample rate for a reconstruction of signal 3401. Thenumber of partition thresholds associated with i partitions of thewaveform 3402 and the threshold levels between partitions are functionsof the required efficiency, limitations of the switched power sourcecircuitry and the pdf associated with the information entropy allocatedto the switched power source function. Nonlinearities of the waveform3402 are effectively suppressed by other discriminating techniques ofthe FLUTTER™ algorithm, as well as filters.

Since switching efficiency η_(sx) can become a design consideration,architectures should take advantage of switch topologies that minimizecascading. Therefore, an example of hierarchical cascading, which isconvenient for binary distributions, is shown in FIG. 35.

For n such cascades the switch efficiency progresses ∝η_(sx) ^(n). Thisquickly siphons energy at the point of delivery and increases wasteentropy S_(w).

As shown in FIG. 35, embodiment 3500 shows three stages 3501, 3503 and3505, defined by boundaries 3507 and 3509, 3511, 3520, 3522, 3524, 3526,3528, and 3530 represent signal paths accessing switching stages 3501,3503, and 3505 respectively. The switching stages are composed of one ormore switching elements 3515, 3516, 3517 and 3518. Although three stagesare illustrated the architecture may continue, accommodating a sequenceof more stages. Furthermore, one stage may suffice for someapplications. Such switching architectures may also be deployed inparallel or series.

Alternatively, parallel switch architectures may be utilized. Thistopology is illustrated as shown in FIG. 36 as embodiment 3600. Source3602 supplies energy or signal or waveform to nodes 3604(a) . . . (n)where “n” is any suitable number, via the switch selection process. An“on” switch 3606(a) . . . (n) can connect nodes 3604(a) . . . (n) tonodes 3608(a) . . . (n). As shown in FIG. 36, each switch possesses a“no connect” (NC) option 3610(a) . . . (n) respectively. In thisembodiment, only one switch may access a power partition or a signal ora waveform 3602 at any given instant and transfer 3602 to 3606(a) . . .(n). The efficiency, of this switch topology is on the order of η_(sx).The load impedances attached to this switch at nodes 3608(a) . . . (n)(outputs), as well as “soft” shut down, and “soft” start must bespecifically tailored for the source at 3602 to avoid deleteriouscontentions and poorly behaved initial conditions when switching betweenoutputs. In some cases the equivalent of a time variable transitionconductance may be employed within the switching circuits in conjunctionwith adjustment of the source at 3602 and the loads connected to theswitch to eliminate transition discontinuities in charge transferthrough various circuit nodes of 3600. Although loads are notillustrated it is understood that suitable impedances may be connectedto nodes 3608(a) . . . (n).

The FLUTTER™ algorithms and its related energy partitioning schemes maybe adapted to traditional RF modulators and transmitters to enhanceefficiency. FLUTTER™ does not require exclusive implementation. FLUTTER™processing algorithms may enhance the efficiency for;

-   -   Polar Architectures    -   Kahn's Technique    -   Envelope Restoration    -   Envelope Tracking    -   LINC    -   Chireix Outphasing    -   Doherty    -   Complex Modulators followed by Amplifier Chains

Indeed, embodiments of the present invention also apply to architecturesthat connect and control with fields and not conductors or switches. Forexample apparatus which use electromagnetic coupling, optical coupling,pressure coupling and combinations thereof.

There are several aspects of FLUTTER™ and the disclosed architecturesthat enable standards based communications applications as well asemerging standards. This includes the support of CDMA, WCDMA, LTE, OFDMbased, GSM, as well as ultra wide band waveforms amongst others. Inaddition, spread spectrum as well as frequency hopped signaling schemesare contemplated in terms of benefits offered by FLUTTER™. In general,an information bearing function of time (signal) may be continuous innature, discrete or a combination. Such signals may be multiplexed toinclude time division multiplexed TDM, frequency division multiplexed(FDM), code division multiple access (CDMA), and hybrid schemes. Thesignals may be pulse modulated as well as pulse width modulated atregular or random intervals of time. The pulses may be of a variety ofshapes such as rectangular, Gaussian, sine-like, etc., symmetric orasymmetric in time. Waveforms which may be modulated to produce thesesignals may be baseband in nature or based on the modulation of localoscillators or other harmonic functions produced through modulation ofcomplex impedances to produce pass band signals as well.

Although much of the discussion includes optimization for informationand energy partitions, it should be apparent to those skilled in the artthat a variety of practical tradeoffs in cost, hardware availability,etc., may on occasion dictate sub optimal partitions which perhapsperform at some lower efficiency. This disclosure has enabled suchtradeoffs, providing the necessary guidance for design compromises usingthe FLUTTER™ algorithm.

FIG. 37 illustrates that FLUTTER™ algorithms may be distributed innature. Embodiment 3700 includes is a set of information inputs 3710with uncertainty {H₁(x), H₂(x) . . . H_(m)(x)}. 3715 is a FLUTTER™ andblended control processor with distributed input-output capability. 3725is a bank of analog compositing functions. 3300 represents amultiplicity of information bearing functions of time, also referred toas output signal 1 through “n” where “n” is any suitable integer.

Multi-channel FLUTTER™ algorithms operate on a set (3710) of informationinputs to render information bearing functions of time or output signalsusing any number of inputs 3710 up to “m” to render any number ofoutputs 3730 up to “n”. There are no restrictions on “n” or “m” otherthan they be integers greater than or equal to one. Furthermore, thecontent of the up to “n” output channels may have some portion ofinformation in part or in whole, in common between each output. Also,each output may be completely unique and independent of the other. Thecompositing process may be any analog or digital processor and utilizesoftware and/or microprocessors.

In another embodiment, blended controls used to access functions anddomains which form statistical composites may access general classes ofmathematical, logical and geometrical functions in any combination whichrepresent sampled data. The representations may be interpolated,extrapolated, and approximated in any combination from data sets usingstructures such as points, lines, line segments, splines, surfaceelements including manifolds, patches, facets and volume elements of anysuitable character. The representations may be in part or in wholederived from a priori data and/or real time information sources, H(x).These structures may be employed homogeneously or in any combination togenerate differential entropy surfaces, differential entropy volumes orsuitable transformations thereof. An differential entropy surface is a 2dimensional representation. A differential entropy volume is a Ddimensional representation where D is an integer greater than or equalto 3. Upon suitable transformation, the resulting compositerepresentations shall be used to render an information bearing functionof time.

FIG. 38 illustrates three examples of some structures which may be usedto form entropy surfaces. These structures are fit to the surface in avariety of polygonal shapes, sizes and dimensions to permit efficientcomputational representation of the surface. Similar structures may beconceived in higher dimension geometries but are difficult to representgraphically.

It should be understood by those skilled in the art that variousmodifications, combinations, sub-combinations and alterations may occurdepending on design requirements and other factors insofar as they arewithin the scope of the appended claims or the equivalents thereof.

The foregoing description of embodiments has been presented for purposesof illustration and description. The foregoing description is notintended to be exhaustive or to limit embodiments of the presentinvention to the precise form disclosed, and modifications andvariations are possible in light of the above teachings or may beacquired from practice of various embodiments.

The embodiments discussed herein were chosen and described in order toexplain the principles and the nature of various embodiments and itspractical application to enable one skilled in the art to utilize thepresent invention in various embodiments and with various modificationsas are suited to the particular use contemplated. The features of theembodiments described herein may be combined in all possiblecombinations of methods, apparatus, modules, systems and computerprogram products.

Having thus described in detail preferred embodiments of the presentinvention, it is to be understood that the invention defined by theabove paragraphs is not to be limited to particular details set forth inthe above description as many apparent variations thereof are possiblewithout departing from the spirit or scope of the present invention.

1-66. (canceled)
 67. A method for allocating one or more than one sourceof information from a set of information (H₁(x), H₂ (x) . . . H_(m)(x))comprising: processing allocated uncertainty of the source ofinformation to form blended controls; identifying one or more degrees offreedom present in the source of information; manipulating degrees offreedom, based on the blended control functions, wherein the degrees offreedom have one or more constituent signals and energy partitions;compositing statistically weighted constituent signals to render aninformation bearing function of time; and allocating the source ofinformation based on the composting step.
 68. The method as claimed in67, wherein the set of information (H₁(x), H₂(x) . . . H_(m)(x)) areutilized in part or whole to render one or more than one informationbearing function of time or other metric, up toil information bearingfunctions of time or metric. 69.-74. (canceled)
 75. A method forrendering a representation of an information bearing function of timecomprising: accessing parameters of a desired information bearingfunction of time, including multiple signals; compositing selected onesof the multiple signals; and rendering a representation of the desiredinformation bearing function of time is based on the compositing step.76. The method as claimed in claim 75, wherein the compositing stepincludes examining a covariance of statistical parameters of a signal ofinterest.
 77. The method as claimed in claim 75, wherein the compositingstep is based on one or more cross-correlations.
 78. The method asclaimed in claim 75, wherein the compositing step includes calculationsof statistical dependencies.
 79. The method as claimed in claim 75,wherein the multiple signals include one or more subsets of signals. 80.The method as claimed in claim 75, wherein the multiple signals comprisethree or more signals.
 81. The method as claimed in claim 75, whereinthe multiple signals comprise two or more from a set of amplitudefunctions and/or magnitude functions and one or more phase functions.82. The method as claimed in claim 81, wherein each of the two or moreamplitude functions have an associated frequency and bandwidth and/orrate.
 83. The method as claimed in claim 82, wherein a first amplitudefunction has a first frequency and a second amplitude function has asecond frequency, and wherein the first frequency does not equal thesecond frequency.
 84. The method as claimed in claim 82, wherein two ormore functions have associated spectral density and frequency spans. 85.The method as claimed in claim 84, wherein a first function has a firstspectral density and associated frequency span and a second function hasa second spectral density and associated frequency span.
 86. The methodas claimed in claim 85, wherein the first spectral density and thesecond spectral density are at least partially independent of oneanother.
 87. The method as claimed in claim 75, wherein therepresentation of the desired information bearing function of time is anRF carrier signal.
 88. The method as claimed in claim 75, wherein theparameters of a desired information bearing function of time are basedon apriori information and/or system characterization.
 89. A method forgenerating an information bearing function of time comprising:identifying one or more characteristics of a desired information bearingfunction of time; identifying selected multiple signals from aninformation source; and synthesizing a representation of the desiredinformation bearing function of time based upon a composition of theselected multiple signals, wherein the representation is a waveformrepresentation of the desired information bearing function of timehaving desired thermodynamic efficiency properties.
 90. The method asclaimed in claim 89, wherein the composition includes examiningcovariance of statistical parameters of a signal of interest.
 91. Themethod as claimed in claim 89, wherein the composition includescross-correlations and/or calculated dependencies.
 92. The method asclaimed in claim 89, wherein the multiple signals include three or moresignals.
 93. The method as claimed in claim 92, wherein the three ormore signals include two or more from a set of amplitude and/ormagnitude functions and one or more phase functions.
 94. The method asclaimed in claim 93, wherein each of the two or more from a set ofamplitude and/or magnitude functions has associated frequencies.
 95. Themethod as claimed in claim 89, wherein the desired information bearingfunction of time includes signals, wave representations or compositewaveforms.
 96. The method as claimed in claim 89 wherein the desiredinformation bearing function of time has: a first amplitude and phasedistribution having a first spectral distribution and frequency span;and a second amplitude and phase distribution having a second spectraldistribution and frequency span, wherein the first spectral distributiondoes not equal the second spectral distribution, and the first frequencyspan may or may not equal the second frequency span.
 97. The method asclaimed in claim 89, wherein the characteristics of a desiredinformation bearing function of time are based on apriori informationand/or characterization.
 98. A method for generating an informationbearing function of time comprising: accessing parameters of a desiredinformation bearing function of time; generating a first subsetrepresentation of the desired information bearing function of time basedon one or more input signals and a first function; comparing the firstsubset representation of the desired information bearing function oftime to the parameters of the desired information bearing function oftime; identifying a differential quantity based on the comparing step;compositing the one or more input signals with additional one or moreinput signals when the differential quantity exceeds a predeterminedthreshold; and generating a second subset representation of the desiredinformation bearing function of time based on the compositing step. 99.The method as claimed in claim 98, wherein the differential quantity isa function of characteristics of the desired information bearingfunction of time.
 100. The method as claimed in claim 99, wherein thedesirable characteristics of the desired information bearing function oftime include one or more of function of amplitude, function of frequencyand/or function of phase.
 101. The method as claimed in claim 98,further comprising: identifying one or more statistics of amplitude,frequency and/or phase; and utilizing the one or more identifiedstatistics in the compositing step.
 102. The method as claimed in claim98, wherein the parameters of a desired information bearing function oftime are based on apriori information and/or characterization.
 103. Themethod as claimed in claim 98, wherein the first subset representationand the second subset representation are based on non-linear functions.104. The method as claimed in claim 98, wherein the parameters of thedesired information bearing function of time include real and imaginarycomponents and/or numbers that are established prior to generating thefirst subset representation of the desired information bearing functionof time.
 105. A method for operating one or more energy sources or powersources comprising: accessing characterizations of an informationbearing function of time; accessing a plurality of input sources thatprovide input signals; compositing two or more of the input signals togenerate a representation of the information bearing function of time;and selecting an operational state of at least one of the one or moreenergy sources or power sources based on the compositing step.
 106. Anapparatus to control one or more energy sources or power sourcescomprising: a storage module adapted to store one or more functions ofcharacteristics of a desired information bearing function of time; afirst processing module adapted to receive one or more input signals andat least one of the functions of characteristics of a desiredinformation bearing function of time and provide a first subset ofoutput signals; a second processing module, operatively coupled to thefirst processing module, adapted to receive one or more input signalsand provide a second subset of output signals; and a third processingmodule, operatively coupled to the second processing module, adapted tocomposite the first subset of output signals with the second subset ofoutput signals to generate a representation of the desired informationbearing function of time.
 107. The apparatus as claimed in claim 106,wherein the first processing module and the second processing moduleposses non-linear operations.
 108. The apparatus as claimed in claim106, further comprising: an output node, operatively coupled to thethird processing module, adapted to receive the representation of thedesired information bearing function of time and provide a linearrepresentation of the desired information bearing function of time. 109.The apparatus as claimed in claim 106, wherein one or more input signalsare reconstituted during compositing. 110.-117. (canceled)
 118. A methodfor rendering a representation of an information bearing function oftime comprising: accessing parameters of a plurality of desiredinformation bearing functions of time; compositing multiple signals foreach of the plurality of desired information bearing functions of time;and generating a representation of each of the plurality of the desiredinformation bearing functions of time as a function of the compositingstep. 119.-126. (canceled)